How do you prove #(tanx-sinx)/(2tanx)=sin^2(x/2)#?

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Answer 1 · 2016-08-23T16:20:58

Refer to the Proof in Explanation.

#"The L.H.S."=(tanx-sinx)/(2tanx)#

#=(sinx/cosx-sinx)/{(2sinx)/cosx}#

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

#={(1-cosx)/cancel(cosx)}(cancel(cosx)/2)#

#=(1-cosx)/2#

Since, #1-cos2theta=2sin^2theta#,

#"The L.H.S."=(2sin^2(x/2))/2=sin^2(x/2)= "The R.H.S."#

Hence, the Proof.

Enjoy Maths.!