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Verify the identity:>>>>>>>

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1-(sin^2 x/1+cosx)=cosx?

asked Mar 19, 2013 in TRIGONOMETRY by andrew Scholar

1 Answer

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1 -(sin2x / 1 + cosx)

Recall: trigonometry formulas sin2x + cos2x =1 then sin2x = 1 - cos2x

= 1 -(1 -cos2x / 1+cosx)

Recall : a2 - b2 = (a - b)(a + b)

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

= 1- [1 - cosx]

Recall : Distributive property a(b - c) = ab - ac

= 1 - 1 +cosx

= 0 +cosx

= cosx

There fore Left hand side = right hand side

1 -(sin^2x / 1 + cosx) = cosx

answered Mar 23, 2013 by diane Scholar

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