Prove 1-sinx/1+sinx=(tanx-secx)power 2?.

2 Answers
Jun 19, 2018

Kindly go through a Proof in the Explanation.

Explanation:

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

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

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

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

#={(1-sinx)/cosx}^2#,

#={1/cosx-sinx/cosx}^2#,

#=(secx-tanx)^2#,

#=(tanx-secx)^2#, as desired!

Jun 19, 2018

Rationalise L.H.S.

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

#=[(1-sinx)^2/cos^2x]#,

#=[1/cos^2x+sin^2x/cos^2x-(2sinx)/(cosx)*1/cosx]#,

#=sec^2x+tan^2x-2tanxsecx#,

#=(tanx-secx)^2#.