Equation {sin ^2}θ = frac{{{x^2} + {y^2}}}{{2xy}},x,y, ne 0 is possible if

English

Gujarati

Hindi

3.Trigonometrical Ratios, Functions and Identities

hard

The equation ${\sin ^2}\theta = \frac{{{x^2} + {y^2}}}{{2xy}},x,y, \ne 0$ is possible if

$x = y$

$x = \, -y$

$2x = y$

none of these

Now, $\sin ^{2} \theta=\frac{x^{2}+y^{2}}{2 x y}$

$\therefore \mathrm{x},$ $y$ have same sign

$\frac{x^{2}+y^{2}}{2 x y}=\frac{1}{2}\left[(\sqrt{\frac{x}{y}}-\sqrt{\frac{y}{x}})^{2}+2\right] \geq 1$

Now, $\sin ^{2} \theta \leq 1 .$

Therefore, $\frac{x^{2}+y^{2}}{2 x y}=1$

$ \Rightarrow x=y$

Standard 11

Mathematics

medium

easy

easy

normal

easy