यदि $\tan x = \frac{{2b}}{{a - c}}(a \ne c),$
$y = a\,{\cos ^2}x + 2b\,\sin x\cos x + c\,{\sin ^2}x$
तथा $z = a{\sin ^2}x - 2b\sin x\cos x + c{\cos ^2}x,$ हो, तब
$y = z$
$y + z = a + c$
$y - z = a + c$
$y - z = {(a - c)^2} + 4{b^2}$
यदि $A = 133^\circ ,$ तब $\;2\cos \frac{A}{2} =$
यदि $\sin A + \cos A = \sqrt 2 ,$ तो ${\cos ^2}A = $
निम्नलिखित को सिद्ध कीजिए
$\frac{\sin x-\sin 3 x}{\sin ^{2} x-\cos ^{2} x}=2 \sin x$
यदि $\tan x + \tan \left( {\frac{\pi }{3} + x} \right) + \tan \left( {\frac{{2\pi }}{3} + x} \right) = 3,$ हो, तब
यदि $\tan A = \frac{1}{2},\tan B = \frac{1}{3},$ तब $\cos 2A = $