Trigonometric identities

Question

(cosx/secx-1) + (cosx/secx+1)

Answer 1

Note that sec x is the reciprocal of cos x, so that

 

cos x / sec x = cos² x.

 

Thus

 

(cos x / sec x - 1) + (cos x / sec x + 1) = (cos² x - 1) + (cos² x + 1) = 2 cos² x.

 

Is this the right problem? It's not really using a trigonometric identity, but rather just the reciprocal relation between cosine and secant.

Answer 2

(cosx/secx) = 1

(1 - 1) + (1 + 1) = 0 + 2 = 2