If x sin^3 alpha + y cos^3 alpha = sin alpha | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equations are:$x \sin^3 \alpha + y \cos^3 \alpha = \sin \alpha \cos \alpha$  --- $(i)$$x \sin \alpha - y \cos \alpha = 0$  --- $(ii)$From eq

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Given equations are:$x \sin^3 \alpha + y \cos^3 \alpha = \sin \alpha \cos \alpha$  --- $(i)$$x \sin \alpha - y \cos \alpha = 0$  --- $(ii)$From equation $(ii)$,we have $x \sin \alpha = y \cos \alpha$.Substitute $x \sin \alpha = y \cos \alpha$ into equation $(i)$:$(x \sin \alpha) \sin^2 \alpha + y \cos^3 \alpha = \sin \alpha \cos \alpha$$(y \cos \alpha) \sin^2 \alpha + y \cos^3 \alpha = \sin \alpha \cos \alpha$$y \cos \alpha (\sin^2 \alpha + \cos^2 \alpha) = \sin \alpha \cos \alpha$Since $\sin^2 \alpha + \cos^2 \alpha = 1$,we get:$y \cos \alpha = \sin \alpha \cos \alpha$Assuming $\cos \alpha 
eq 0$,we get $y = \sin \alpha$.Substituting $y = \sin \alpha$ into $x \sin \alpha = y \cos \alpha$,we get $x \sin \alpha = \sin \alpha \cos \alpha$,which implies $x = \cos \alpha$.Therefore,$x^2 + y^2 = \cos^2 \alpha + \sin^2 \alpha = 1$.

If $x \sin^3 \alpha + y \cos^3 \alpha = \sin \alpha \cos \alpha$ and $x \sin \alpha - y \cos \alpha = 0$,then $x^2 + y^2 = $

Similar Questions

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$,then $\cos 2A = $

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

The value of $\frac{\tan x}{\tan 3x}$,whenever defined,never lies between:

If $\sin \theta = \frac{12}{13}$ where $0 < \theta < \frac{\pi}{2}$ and $\cos \phi = -\frac{3}{5}$ where $\pi < \phi < \frac{3\pi}{2}$,then $\sin(\theta + \phi)$ is:

If $A$ lies in the second quadrant and $B$ lies in the third quadrant and $\cos A = -\frac{\sqrt{3}}{2}$ and $\sin B = -\frac{3}{5}$,then find the value of $\frac{2 \tan B + \sqrt{3} \tan A}{\cot^2 A + \cos B}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module