Verify the identity:>>>>>>>

Question

 

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

Answer 1

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