147 lines
3.0 KiB
Plaintext
147 lines
3.0 KiB
Plaintext
ans
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018366
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(1) $x=\dfrac{\pi}{3}+2k\pi$或$\dfrac{2\pi}{3}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{3\pi}{4}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$
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018367
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(1) $\{\dfrac{\pi}{6},\dfrac{\pi}{3},\dfrac{7\pi}{6},\dfrac{4\pi}{3}\}$; (2) $\{x|x=2k\pi+\dfrac{\pi}{12}\text{或}x=2k\pi-\dfrac{5\pi}{12}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$
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018369
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(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$
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009563
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(1) $\{\dfrac{\pi}{2},\dfrac{11\pi}{6}\}$; (2) $\{x|x=k\pi+\dfrac{5\pi}{24}\text{或}k\pi-\dfrac{11\pi}{24}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$
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018372
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$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$
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018373
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$-\dfrac{56}{65}$
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018375
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$\dfrac{\pi}{3}$
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009564
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(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$
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009565
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$-\dfrac{7\sqrt{2}}{26}$
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018377
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(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$
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018376
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$-\dfrac{4}{5}$
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018378
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$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
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018379
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证明略
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018380
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(1) $-1$; (2) $\dfrac{1}{7}$
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018381
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$-\sqrt{3}$
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009567
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(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$
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009568
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$\dfrac{\sqrt{2}}{10}$, $7$
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009569
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(1) 证明略; (2) 证明略
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018385
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证明略
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018386
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$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$
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018387
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(1) $\sin(\alpha+\dfrac{\pi}{3})$; (2) $\sqrt{2}\sin(\alpha-\dfrac{\pi}{4})$; (3) $5\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{3}{5}$, $\sin\varphi=\dfrac{4}{5}$; (4) $\sqrt{a^2+b^2}\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$
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024614
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$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$
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009570
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$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$
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009571
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$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角
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009572
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(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$
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018390
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$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
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018393
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$\sin 2\alpha=-\dfrac{24}{25}$, $\cos 2\alpha = -\dfrac{7}{25}$, $\tan 2\alpha = \dfrac{24}{7}$
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018395
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$\cos 3\theta = 4\cos^3\theta-3\cos \theta$
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018396
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(1) 证明略; (2) 证明略
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009573
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(1) $\dfrac{1}{4}$; (2) $\dfrac{\sqrt{2}}{2}$; (3) $\dfrac{\sqrt{3}}{6}$
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018394
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$\sin 4\alpha=\dfrac{336}{625}$; $\cos 4\alpha = -\dfrac{527}{625}$
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009574
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$\sin 2\alpha=-\dfrac{4}{5}$, $\cos 2\alpha=-\dfrac{3}{5}$, $\tan 2\alpha=\dfrac{4}{3}$
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009575
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(1) 证明略; (2) 证明略; (3) 证明略
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018398
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$\dfrac{7}{25}$
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018401
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$\cos ^2 \dfrac{\alpha}{2}=\dfrac{1+\cos\alpha}{2}$, $\sin ^2 \dfrac{\alpha}{2}=\dfrac{1-\cos\alpha}{2}$, $\tan ^2 \dfrac{\alpha}{2}=\dfrac{1-\cos\alpha}{1+\cos\alpha}$
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018402
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证明略
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018403
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证明略
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018404
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证明略
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009576
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证明略
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009577
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证明略
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009578
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证明略
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018405
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证明略
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040387
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$\dfrac{5\pi}{3}$
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040388
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$-1$
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040389
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$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$
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040390
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$-3$
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040391
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$-2$
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040392
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$-\dfrac{\sqrt{23}}{4}$
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