Question #a4298

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Answer 1 · 2017-12-25T06:29:10

Kindly refer to the Explanation.

#"Prerequisites : "(1) : 1+cos2theta=2cos^2theta,#

# : (2) : 1-cos2theta=2sin^2theta#.

#cot^2(pi/4+x/2)=(cos^2(pi/4+x/2))/sin^2(pi/4+x/2)#,

#=(2cos^2(pi/4+x/2))/(2sin^2(pi/4+x/2)#,

#={1+cos(2(pi/4+x/2))}/{1-cos(2(pi/4+x/2))}#,

#=(1+cos(pi/2+x))/(1-cos(pi/2+x))#,

#=(1-sinx)/{1-(-sinx)}=(1-sinx)/(1+sinx)#,

#={1/cosx(1-sinx)}/{1/cosx(1+sinx)}#,

#=(1/cosx-sinx/cosx)/(1/cosx+sinx/cosx)#,

#=(secx-tanx)/(secx+tanx)#.

Q.E.D.

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