If sin θ = frac{1}{2}left( {√ {frac{x}{y},} + ,√ {frac{y}{x}} } right),,,left( {x,y

English

Gujarati

Hindi

3.Trigonometrical Ratios, Functions and Identities

normal

If $\sin \theta = \frac{1}{2}\left( {\sqrt {\frac{x}{y}\,} + \,\sqrt {\frac{y}{x}} } \right)\,,\,\left( {x,y \in R\, - \{ 0\} } \right)$. Then

A

$x=y$

B

$ x < y $

C

$x>y$

D

$x+y$ = $1\ \forall\ x,y \in R$

Solution

$\frac{1}{2}\left( {\sqrt {\frac{x}{y}} + \sqrt {\frac{y}{x}} } \right) \ge 1$

$\Rightarrow \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=2$

$ \Rightarrow x=y$

Standard 11

Mathematics

Share

Similar Questions

If ${\rm{cosec}}\theta = \frac{{p + q}}{{p – q}},$ then $\cot \,\left( {\frac{\pi }{4} + \frac{\theta }{2}} \right) = $

medium

$cot 5^o$ -$tan5^o$ -$2$ $tan10^o$ -$4$ $tan 20^o$ -$8$ $cot40^o$ is equal to

normal

If $A + B + C = {180^o},$ then the value of $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}$ will be

medium

If $2\tan A = 3\tan B,$ then $\frac{{\sin 2B}}{{5 – \cos 2B}}$ is equal to

medium

Prove that $\tan 4 x=\frac{4 \tan x\left(1-\tan ^{2} x\right)}{1-6 \tan ^{2} x+\tan ^{4} x}$

medium