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.!

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