How do you prove # 2tan(x)sec(x) = (cos^2x+sin^2x)/(1-sin(x)) - (1/(1+sin(x))) #?

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Answer 1 · 2018-03-06T04:39:34

Please refer to a Proof in the Explanation.

Since, #cos^2x+sin^2x=1#, we have,

#(cos^2x+sin^2x)/(1-sinx)-1/(1+sinx)#,

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

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

#=(1+sinx-1+sinx)/(1-sin^2x)#,

#=(2sinx)/cos^2x#,

#=2*sinx/cosx*1/cosx#,

#=2tanxsecx,# as desired!