Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMix Examples-Trigonometrical Ratios, Functions and Identities
EasyIf $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is
- A$10$
- B$2^{10}$
- C$2^9$
- D$2$
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Similar Questions
For $0 < \theta < \frac{\pi}{2}$,the solution$(s)$ of $\sum_{m=1}^6 \operatorname{cosec}\left(\theta+\frac{(m-1) \pi}{4}\right) \operatorname{cosec}\left(\theta+\frac{m \pi}{4}\right) = 4 \sqrt{2}$ is(are):
Match the items of List-$I$ to the items of List-$II$:
List-$I$ List-$II$ $A$. The period of $\sin^2 x$ is $I$. $\frac{2\pi}{3}$ $B$. Maximum value of $\frac{\pi}{3}(\sqrt{3}\cos 3x + \sin 3x)$ $II$. $12\pi$ $C$. The period of $\sin \frac{x}{3} + \cos \frac{x}{2}$ is $III$. $\frac{\pi}{2}$ $D$. Intersection points of $y=|\sin x|$ and $y=1$ in $(0, \pi)$ $IV$. $\frac{3\pi}{2}$ $V$. $\pi$
| List-$I$ | List-$II$ |
| $A$. The period of $\sin^2 x$ is | $I$. $\frac{2\pi}{3}$ |
| $B$. Maximum value of $\frac{\pi}{3}(\sqrt{3}\cos 3x + \sin 3x)$ | $II$. $12\pi$ |
| $C$. The period of $\sin \frac{x}{3} + \cos \frac{x}{2}$ is | $III$. $\frac{\pi}{2}$ |
| $D$. Intersection points of $y=|\sin x|$ and $y=1$ in $(0, \pi)$ | $IV$. $\frac{3\pi}{2}$ |
| $V$. $\pi$ |
If $\frac{\tan (\alpha+\beta-\gamma)}{\tan (\alpha-\beta+\gamma)}=\frac{\tan \gamma}{\tan \beta}$ and $\beta \neq \gamma$,then the value of $\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma$ is
$\cos \frac{2\pi}{15} \cos \frac{4\pi}{15} \cos \frac{8\pi}{15} \cos \frac{16\pi}{15} = $
MediumIIT 1985
View Solution$\sinh (x+y) \cosh (x-y)$ is equal to
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