Given that pi

Question

(A) Given $\pi < \alpha < \frac{3\pi}{2},$ $\alpha$ lies in the third quadrant.Simplify the expression: $\sqrt{4\sin^4 \alpha + \sin^2 2\alpha} + 4\co

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Given $\pi Simplify the expression: $\sqrt{4\sin^4 \alpha + \sin^2 2\alpha} + 4\cos^2 \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$$= \sqrt{4\sin^4 \alpha + 4\sin^2 \alpha \cos^2 \alpha} + 2 \left[ 2\cos^2 \left( \frac{\pi}{4} - \frac{\alpha}{2} \right) \right]$$= \sqrt{4\sin^2 \alpha (\sin^2 \alpha + \cos^2 \alpha)} + 2 \left[ 1 + \cos \left( \frac{\pi}{2} - \alpha \right) \right]$$= \sqrt{4\sin^2 \alpha} + 2(1 + \sin \alpha) = 2|\sin \alpha| + 2 + 2\sin \alpha$Since $\pi Expression $= 2(-\sin \alpha) + 2 + 2\sin \alpha = 2$.

Given that $\pi < \alpha < \frac{3\pi}{2},$ then the expression $\sqrt{4\sin^4 \alpha + \sin^2 2\alpha} + 4\cos^2 \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$ is equal to

Similar Questions

If $A = 130^\circ$ and $x = \sin A + \cos A$,then

If $\sin \theta + \csc \theta = 2$,then $\sin^2 \theta + \csc^2 \theta = $

If $2 \sin \left(\frac{\pi}{2}\right) = x^{2} + \frac{1}{x^{2}}$,then the value of $\left(x - \frac{1}{x}\right)$ is

To an observer on the ground,the angle of elevation of the top of a tower is $30^{\circ}$. If the height of the tower is $100 \ m$,find the distance between the top of the tower and the point of observation (in meters).

If $\sin (\theta + \alpha ) = a$ and $\sin (\theta + \beta ) = b,$ then $\cos 2(\alpha - \beta ) - 4ab\cos (\alpha - \beta )$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module