સાબિત કરો કે : $(\cos x+\cos y)^{2}+(\sin x-\sin y)^{2}=4 \cos ^{2} \frac{x+y}{2}$
$L.H.S.$ $=(\cos x+\cos y)^{2}+(\sin x-\sin y)^{2}$
$=\cos ^{2} x+\cos ^{2} y+2 \cos x \cos y+\sin ^{2} x+\sin ^{2} y-2 \sin x \sin y$
$=\left(\cos ^{2} x+\sin ^{2} x\right)+\left(\cos ^{2} y+\sin ^{2} y\right)+2(\cos x \cos y-\sin x \sin y)$
$=1+1+2 \cos (x+y) \quad[\cos (A+B)=(\cos A \cos B-\sin A \sin B)]$
$=2+2 \cos (x+y)$
$=2[1+\cos (x+y)]$
$=2\left[1+2 \cos ^{2}\left(\frac{x+y}{2}\right)-1\right] \quad\left[\cos 2 A=2 \cos ^{2} A-1\right]$
$=4 \cos ^{2}\left(\frac{x+y}{2}\right)= R.H . S.$
$6({\sin ^6}\theta + {\cos ^6}\theta ) - 9({\sin ^4}\theta + {\cos ^4}\theta ) + 4 = . . . $
અંશ માપ શોધો. ( $\pi=\frac{22}{7}$ લો. ) $-4$
જો $\cos \theta = \frac{1}{2}\left( {x + \frac{1}{x}} \right)$, તો $\frac{1}{2}\left( {{x^2} + \frac{1}{{{x^2}}}} \right) = $
જો $\tan \theta = - \frac{1}{{\sqrt {10} }}$ અને $\theta $ એ ચોથા ચરણમાં હોય તો $\cos \theta = $
સાબિત કરો કે : $2 \sin ^{2} \frac{\pi}{6}+\cos ec ^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}$