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

Prove : $\cos^22x-\cos^26x=\sin 4x.\sin 8x$

1 Answer

Toolbox:
  • $\cos^2A=1-\sin^2A$
  • $\sin^2A-\sin^2B=\sin(A+B).\sin (A-B)$
L.H.S
$\cos^22x-\cos^26x=1-\sin^22x-(1-\sin^26x)$
$\Rightarrow 1-\sin^22x-1+\sin^26x$
$\Rightarrow \sin^26x-\sin^22x$
$\Rightarrow \sin(6x+2x).\sin (6x-2x)$
$\Rightarrow \sin 8x.\sin 4x$=R.H.S
Hence proved.
answered Apr 17, 2014 by sreemathi.v
 
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