If sin 2theta + sin 2phi = 1/2 and cos 2theta | vedclass

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

Question

(B) Given equations are:$\sin 2	heta + \sin 2\phi = 1/2$  --- $(i)$$\cos 2	heta + \cos 2\phi = 3/2$  --- $(ii)$Squaring and adding equations $(i)$ a

Vedclass · Accepted Answer

$5/8$

Vedclass · Answer

(B) Given equations are:$\sin 2	heta + \sin 2\phi = 1/2$  --- $(i)$$\cos 2	heta + \cos 2\phi = 3/2$  --- $(ii)$Squaring and adding equations $(i)$ and $(ii)$:$(\sin 2	heta + \sin 2\phi)^2 + (\cos 2	heta + \cos 2\phi)^2 = (1/2)^2 + (3/2)^2$$(\sin^2 2	heta + \cos^2 2	heta) + (\sin^2 2\phi + \cos^2 2\phi) + 2(\sin 2	heta \sin 2\phi + \cos 2	heta \cos 2\phi) = 1/4 + 9/4$$1 + 1 + 2 \cos(2	heta - 2\phi) = 10/4$$2 + 2 \cos(2	heta - 2\phi) = 5/2$$2 \cos(2	heta - 2\phi) = 5/2 - 2 = 1/2$$\cos(2	heta - 2\phi) = 1/4$Using the identity $\cos 2A = 2 \cos^2 A - 1$:$2 \cos^2(	heta - \phi) - 1 = 1/4$$2 \cos^2(	heta - \phi) = 1 + 1/4 = 5/4$$\cos^2(	heta - \phi) = 5/8$.

If $\sin 2\theta + \sin 2\phi = 1/2$ and $\cos 2\theta + \cos 2\phi = 3/2$,then $\cos^2(\theta - \phi) = $

Similar Questions

The value of $\cos 15^\circ - \sin 15^\circ$ is equal to

$\frac{{\cos {{10}^o} + \sin {{10}^o}}}{{\cos {{10}^o} - \sin {{10}^o}}} = $

Choose the $INCORRECT$ statement$(s)$.

$\frac{\sin 81^\circ + \cos 81^\circ}{\sin 81^\circ - \cos 81^\circ}$ is equal to

If $\cos(\alpha + \beta) = \frac{4}{5}$ and $\sin(\alpha - \beta) = \frac{5}{13}$,where $0 \le \alpha, \beta \le \frac{\pi}{4}$. Then $\tan 2\alpha = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module