If cos(alpha + beta) = 0,then sin(alpha + 2be | vedclass

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

Question

(A) Given $\cos(\alpha + \beta) = 0$.Since $\cos(	heta) = 0$ implies $	heta = \frac{\pi}{2} + n\pi$,we take the principal value $\alpha + \beta = \f

Vedclass · Accepted Answer

$\sin \alpha$

Vedclass · Answer

(A) Given $\cos(\alpha + \beta) = 0$.Since $\cos(	heta) = 0$ implies $	heta = \frac{\pi}{2} + n\pi$,we take the principal value $\alpha + \beta = \frac{\pi}{2}$.Thus,$\beta = \frac{\pi}{2} - \alpha$.Now,substitute $\beta$ into the expression $\sin(\alpha + 2\beta)$:$\sin(\alpha + 2(\frac{\pi}{2} - \alpha)) = \sin(\alpha + \pi - 2\alpha) = \sin(\pi - \alpha)$.Using the identity $\sin(\pi - 	heta) = \sin 	heta$,we get $\sin(\pi - \alpha) = \sin \alpha$.

If $\cos(\alpha + \beta) = 0$,then $\sin(\alpha + 2\beta) =$

Similar Questions

If $\sin A = \frac{-7}{25}$,$\cos B = \frac{8}{17}$,$A$ does not lie in the $3^{\text{rd}}$ quadrant and $B$ does not lie in the $1^{\text{st}}$ quadrant,then $8 \tan A - 5 \cot B =$

Find the radian measure corresponding to the following degree measure: $240^{\circ}$

Find the value of $\cos \left(-1710^{\circ}\right)$.

$\cot (45^\circ + \theta ) \cot (45^\circ - \theta ) = $

Which of the following have the same value?
$(a)$ $\sin 120^{\circ}$
$(b)$ $\cos 930^{\circ}$
$(c)$ $\tan 840^{\circ}$
$(d)$ $\cot (-1110^{\circ})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module