Question

cos x minus sin y whole square + sin x minus sin y whole square equal to 4 cos square​

Answer 1

Answer:

question is incomplete,, 4 cos square???

Answer 2

$(\cos x+\cos y)^{2} +(\sin x-\sin y)^{2}=2\cos^2 \dfrac{x+y}{2}$, proved.

Step-by-step explanation:

$L.H.S.=(\cos x+\cos y)^{2} +(\sin x-\sin y)^{2}$

$=\cos^2 x+\cos^2 y+2\cos x\cos y+\sin^2 x+\sin^2 y-2\sin x\sin y$

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

$=1+1+2\cos x\cos y-2\sin x\sin y$

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

$=2+2\cos (x+y)$

[ ∵ $\cos (A+B)=\cos A\cos B-\sin A\sin B$]

$=2(1+\cos (x+y)$

$=2\cos^2 \dfrac{x+y}{2}$

[ ∵ $2\cos^2 \dfrac{A+B}{2}=1+\cos (A+B)$

=R.H.S, proved.

Hence,$(\cos x+\cos y)^{2} +(\sin x-\sin y)^{2}=2\cos^2 \dfrac{x+y}{2}$, proved.

you can refer:

https://brainly.in/question/2569880