CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$x + y = \pi + z$$, then prove that $$\sin^2 x + \sin^2 y - \sin^2 z = 2 \sin x \sin y \cos z$$.


Solution

$$ x+y = \pi +z$$

$$\Rightarrow$$$$ z = x+y - \pi$$

$$\Rightarrow \sin^{2} x+\sin^{2}y-\sin^{2}z$$
$$=\sin^{2}x +\sin^{2}y- \sin^{2}(x+y- \pi)$$

$$=\sin^{2}x +\sin^{2}y-\sin^{2}(x+y)$$

$$=\sin^{2}x+ \sin(-x)\times \sin(x+2y)$$

$$=\sin x \times(\sin x -\sin(x+2y))$$

$$=\sin x \times 2\times \cos(x+y)\times \sin(-y)$$

$$=2\sin x$$ $$\sin y$$ $$\cos z$$

L.H.S.= R.H.S.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image