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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions

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

1 Answer

Toolbox:
  • $\cos A+\cos B=2\cos \large\frac{A+B}{2}$$\cos \large\frac{A-B}{2}$
  • $\sin A-\sin B=2\cos \large\frac{A+B}{2}$$\sin \large\frac{A-B}{2}$
L.H.S
$(\cos x+\cos y)^2+(\sin x-\sin y)^2$
$(2\cos\large\frac{x+y}{2}$$.\cos \large\frac{x-y}{2})^2+$$(2\cos^2\large\frac{x+y}{2}$$\sin^2\large\frac{x-y}{2})^2$
$4\cos^2\large\frac{x+y}{2}$$.\cos^2\large\frac{x-y}{2}$$+4\cos^2\large\frac{x+y}{2}$$.\sin^2\large\frac{x-y}{2}$
$4\cos^2\large\frac{x+y}{2}$$\big(\cos^2\large\frac{x-y}{2}$$+\sin^2\large\frac{x-y}{2}\big)$
$\sin^2A+\cos^2A=1$
$4\cos^2\large\frac{x+y}{2}$$\times 1=4\cos^2\large\frac{x+y}{2}$=R.H.S
Hence proved.
answered Apr 18, 2014 by sreemathi.v
 

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