Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMix Examples-Trigonometrical Ratios, Functions and Identities
MediumIf $\sin A = n \sin (A + 2B)$,then $\tan (A + B) =$
- A$\frac{1+n}{1-n} \tan B$
- B$\frac{1-n}{1+n} \tan B$
- C$\frac{1+n}{n-1} \tan B$
- D$\frac{n-1}{n+1} \tan B$
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Similar Questions
If $|\sin \alpha - \cos \alpha| = \frac{3}{4}$,then $|\sec 2\alpha - \tan 2\alpha| = $
If $\tan x = \frac{b}{a},$ then $\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}} = $
Easy
View SolutionMatch 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 $(0, \pi)$ | $IV$. $\frac{3\pi}{2}$ |
| $V$. $\pi$ |
$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $
DifficultIIT 1984
View SolutionIf $\operatorname{Sinh}^{-1} x = \operatorname{Cosh}^{-1} y = \log(1+\sqrt{2})$, then $\operatorname{Tan}^{-1}(x+y) = $
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