If cosx cos(pi/7) + sinx sin(pi/7) = -(sqrt(2))/2, then x can (check all that apply) (will give medal & fan! ) a. pi/4 + pi/7 + 2npi b. 5pi/4 + pi/7 + 2npi c. 7pi/4 + pi/7 + 2npi d. 3pi/4 + pi/7 + 2npi

The answer is below

Step-by-step explanation:

Trigonometric identities are ratios used to show the relationship between the sides and angles in a right angled triangle. Some trigonometric identities are:

sinθ = opposite / hypotenuse; cosθ = adjacent / hypotenuse; tanθ = opposite / adjacent

From the image, let a be the hypotenuse, hence:

a² = 15² + 8²

a² = 225 + 64

a² = 289

a = 17

From the triangle:

90 + x + y = 180 (sum of angle in a triangle)

x + y = 90

It is stated that for a right angled triangle, if x + y = 90 (complementary angles) then:

sinx = cosy

To prove:

sinx = 8/17; cosy = 8/17. Hence:

sinx = cosy