Establish the identity. (6cosθ−7sinθ)^2 + (7cosθ+6sinθ)^2 = 85

Question

Rewrite the left side by removing the parentheses.

? + 49 cos²θ + 84 cos θ sin θ + 36 sin²θ

Rewrite the expression found in the previous step by combining like terms.

? (Do not factor.)

Rewrite the expression found in the previous step by factoring out the common term.

?

The expression from the previous step then simplifies to 85 using​ what?

A. Even-Odd Identity.

B. Quotient Identity.

C. Reciprocal Identity.

D. Pythagorean Identity.

E. Cancellation Identity.

Answer 1

(6C-7S)^2 + (7C+6S)

= 36C^2 -42CS +49S^2 + 49C^2 +42CS + 36S^2

C=Cos(Theta), S=Sin(Theta)

36C^2 + 49C^2 = 85C^2, 49S^2 +36S^2 = 85S^2

= 85C^2 + 85S^2

=85(C^2 + S^2)

use the Pythagorean Theorem x^2+y^2 = 1 where Cos(Theta) = x and Sin(Theta) = y

= 85(1)

= 85