Use the cofunction identities to evaluate the expression without using a calculator.
Cos²65° + cos²25°

Question

Use the cofunction identities to evaluate the expression without using a calculator. Cos²65° + cos²25° A)3 B)4 C)-3 D)-1 E)1

Quizplus · Accepted Answer

The cofunction identity for cosine and sine states that cos(θ) = sin(90° - θ). Therefore, cos(65°) = sin(25°) and cos(25°) = sin(65°). Since sine and cosine are cofunctions of each other, the values of sin(25°) and sin(65°) are equal to the cosines of their complementary angles, making the expression equivalent to sin(25°) + sin(65°). Both of these are positive and less than 1, so their sum cannot be an integer. The only non-integer option given is 1, which is the correct choice by process of elimination and understanding of trigonometric properties.

Use the Cofunction Identities to Evaluate the Expression Without Using