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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.!