Sections:

Trigonometric Identities and Equations, Page 13

Examples (continued)

Example 3:

Verify that the equation below is a trigonometric identity. 

1/(tan x + sec x) = cos x/(sin x + 1)

Procedure:

  1. Transform the more complicated side.
  2. Substitute any trigonometric identities that simplify an expression.
  3. Try to put all trigonometric functions in terms of sine and cosine to make it easier to factor or multiply.

Solution:

1/(sin x/cos x + 1/cos x) = cos x/(sin x + 1); 1/((sin x + 1)/cos x) * (cos x/(sin x + 1))/(cos x/(sin x+ 1)) = cos x/(sin x + 1); cos x/(sin x + 1) = cos x/(sin x + 1)