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Trig Equation Problem?

0 votes

Prove:

[sin^2(x)/(1+cos(x))^2]+1 = 2/1+cos(x)

Thanks!!!  

asked Nov 13, 2013 in TRIGONOMETRY by andrew Scholar

1 Answer

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Left hand side =

= [sin^2x/(1+cos(x))^2]+1

From the trigonometric identities sin^2x +cos^2x = 1

= [(1-cos^2x)/(1+cosx)^2]+1

a^2-b^2 = (a+b)(a-b)

consider a = 1, b = cos^2x

= [((1-cosx)(1+cosx))/(1+cosx)(1+cosx)]+1

Cancel the common term(1+cosx)

= [(1-cosx)/(1+cosx)]+1

= 1-cosx+1+cosx/1+cosx

= 2/1+cosx

= Right hand side

answered Nov 13, 2013 by william Mentor

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