Question

Condense (cos92°)(cos133°)-(sin92°)(sin133°) into a singular trigonometric function expression, then find the exact value.

Answer 1

-1/√2

Explanation:

According to trigonometry identity

cos(A+B) = cosAcosB - sinA sinB

Given the expression

(cos92°)(cos133°)-(sin92°)(sin133°)

This can be expressed as cos(92+133) where A = 92, B = 133

(cos92°)(cos133°)-(sin92°)(sin133°)

= cos(92+133)

= cos225

= -0.7071

= -1/√2

Hence the exact value is -1/√2