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Answer 1 · 2016-08-25T16:04:06

See Explanation.

Ex. (1) :

The R.H.S. $=ul(1-cos^2theta)+sin2theta$

$=sin^2theta+2sinthetacostheta$ = The L.H.S.

Ex.(2) :

The L.H.S. $=(sin2x)/(1+cos2x)=(2sinxcosx)/(2cos^2 x)$

$=sinx/cosx=tanx=$ The R.H.S.

Ex.(3) :

The L.H.S. $=tantheta+cottheta-2csc2theta$

$=sintheta/costheta+costheta/sintheta-2csc2theta$

$=(sin^2theta+cos^2theta)/(sinthetacostheta)-2csc2theta$

$=1/(sinthetacostheta)-2csc 2theta$

$=2/(2sinthetacostheta)-2csc2theta$

$=2/(sin2theta)-2csc2theta$

$=2csc2theta-2csc2theta$

$=0=$ The R.H.S.

Enjoy Maths.!