Use the cofunction identities to evaluate the expression without using a calculator.
Cos²35° + cos²50° + cos²40° + cos²55°

Question

Use the cofunction identities to evaluate the expression without using a calculator. Cos²35° + cos²50° + cos²40° + cos²55° A)-2 B)1 C)-1 D)3 E)2

Quizplus · Accepted Answer

The given expression simplifies using the cofunction identity cos(90° - θ) = sin(θ). Thus, cos(35°) = sin(55°), cos(50°) = sin(40°), cos(40°) = sin(50°), and cos(55°) = sin(35°). Since sin(θ) = sin(90° - θ), pairs of these terms are equal, leading to the sum being 2.

Use the Cofunction Identities to Evaluate the Expression Without Using