Prove the following?

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Answer 1 · 2017-08-19T16:09:33

#tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha)#

#=>cottheta=(sinalpha+cosalpha)/(sinalpha-cosalpha)#

#=>cot^2theta+1=(sinalpha+cosalpha)^2/(sinalpha-cosalpha)^2+1#

#=>csc^2theta=((sinalpha+cosalpha)^2+(sinalpha-cosalpha)^2)/(sinalpha-cosalpha)^2#

#=>1/sin^2theta=(2(sin^2alpha+cos^2alpha)^2)/(sinalpha-cosalpha)^2#

#=>2sin^2theta=(sinalpha-cosalpha)^2#

#=>sqrt2sintheta=sinalpha-cosalpha#

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Again

#tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha)#

#=>tan^2theta+1=(sinalpha-cosalpha)^2/(sinalpha+cosalpha)^2+1#

#=>sec^2theta=((sinalpha-cosalpha)^2+(sinalpha+cosalpha)^2)/(sinalpha+cosalpha)^2#

#=>1/cos^2theta=(2(sin^2alpha+cos^2alpha)^2)/(sinalpha+cosalpha)^2#

#=>2cos^2theta=(sinalpha+cosalpha)^2#

#=>sqrt2costheta=sinalpha+cosalpha#