If sin A + sin 2A = x and cos A + cos 2A = y, | vedclass

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

Question

(A) Given: $x = \sin A + \sin 2A$ and $y = \cos A + \cos 2A$.Calculate $x^2 + y^2$:$x^2 + y^2 = (\sin A + \sin 2A)^2 + (\cos A + \cos 2A)^2$$= \sin^2

Vedclass · Accepted Answer

$2y$

Vedclass · Answer

(A) Given: $x = \sin A + \sin 2A$ and $y = \cos A + \cos 2A$.Calculate $x^2 + y^2$:$x^2 + y^2 = (\sin A + \sin 2A)^2 + (\cos A + \cos 2A)^2$$= \sin^2 A + \sin^2 2A + 2 \sin A \sin 2A + \cos^2 A + \cos^2 2A + 2 \cos A \cos 2A$$= (\sin^2 A + \cos^2 A) + (\sin^2 2A + \cos^2 2A) + 2(\cos 2A \cos A + \sin 2A \sin A)$$= 1 + 1 + 2 \cos(2A - A)$$= 2 + 2 \cos A = 2(1 + \cos A)$.Now,substitute this into the expression $({x^2} + {y^2})({x^2} + {y^2} - 3)$:$= [2(1 + \cos A)][2(1 + \cos A) - 3]$$= [2(1 + \cos A)][2 + 2 \cos A - 3]$$= [2(1 + \cos A)][2 \cos A - 1]$$= 2(2 \cos^2 A + \cos A - 1)$$= 2(2 \cos^2 A - 1 + \cos A)$$= 2(\cos 2A + \cos A) = 2y$.

If $\sin A + \sin 2A = x$ and $\cos A + \cos 2A = y,$ then $({x^2} + {y^2})({x^2} + {y^2} - 3) = $

Similar Questions

If $\log_a b + \log_b c + \log_c a$ vanishes,where $a, b,$ and $c$ are positive real numbers different from unity,then the value of $(\log_a b)^3 + (\log_b c)^3 + (\log_c a)^3$ is

$A$ man observes the angle of elevation of the top of a tower having a height of $100 \, m$ as $30^{\circ}$. After walking a certain distance towards the tower,he observes the angle of elevation as $45^{\circ}$. What is the distance through which the man walked towards the tower? (in $m$)

$\cos A + \sin (270^\circ + A) - \sin (270^\circ - A) + \cos (180^\circ + A) = $

The value of $k$,for which $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0$ is an identity,is

If $\tan A = n \tan B$ and $\sin A = m \sin B ,$ then the value of $\cos ^{2} A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module