Embibe Experts Solutions for Exercise 8: Assignment

Let $a$ and $b$ be real numbers such that $\sin a+\sin b=\frac{1}{\sqrt{2}}, \cos a+\cos b=\sqrt{\frac{3}{2}}$, then

If $\cos \alpha +\cos \beta +\cos \gamma =0=\sin \alpha +\sin \beta +\sin \gamma$, then

If $\alpha \in \left[-2\pi , 2\pi \right]$ and $\cos \left(\frac{\alpha }{2}\right)+\sin \left(\frac{\alpha }{2}\right)=\sqrt{2}\left(\cos 36°-\sin 18°\right)$, then the value of $\alpha$ is

The equation $\sin x+\sqrt{3}\cos x=\sqrt{2}$ is satisfied by value of $x$ which is equal to

The equation $\sin x+\sin 2x+2\sin x\sin 2x=2\cos x+\cos 2x$ is satisfied by values of $x$ for which

The solution set of $\sin 3\theta +\cos 2\theta =-2$ is

The general solution of the equation $2^{\cos 2x}+1=3\cdot {\left(2\right)}^{-{\sin }^{2}x}$ is

$\left(m+2\right)\sin \theta +\left(2m-1\right)\cos \theta =2m+1,$ if