SSC CHSL 7 Jan 2017 Shift 3 Paper

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Question : 53 of 100

Marks: +1, -0

If

√{(1+CosA)/2}=x

,then find the value of x.

sin(A/2)
tan(A/2)
cot(A/2)
cos(A/2)

Solution:

Using double angle formula, we know that

cos(2θ)=cos^2θ-sin^2θ

⇒cos(2θ)=cos^2θ-(1-cos^2θ)

⇒cos(2θ)=2cos^2θ- 1

Replacing θ by

A/2

, we get :

⇒cosA=2cos^2 (A/2) -1

⇒cosA+1=2cos^2 (A/2)

⇒{(cosA+1)/2}=cos^2(A/2)

⇒{√(1+cosA )/2}=cos(A/2)

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