Question

Which angle proves this is not an identity?

sα=sinα⋅cos^2α

A. 0 degrees
B. 90 degrees
C. 135 degrees
D. 270 degrees

Answer 1

The angle that proves sα = sinα · cos2α is not an identity is B. 90 degrees, since sin(90) = 1 and cos(90) = 0, making the equation not hold true.

Step-by-step explanation:

The question is asking about trigonometric identities and which angle proves that the given expression sα = sinα · cos2α is not an identity. To find out, we substitute each provided angle into the equation and see if both sides are equal.

• For 0 degrees, sin(0) = 0, so the right-hand side of the equation would be 0. This is the same as the left-hand side, sα = s(0) which equals to 0.
• For 90 degrees, sin(90) = 1, but cos(90) = 0, so the right-hand side of the equation would be 0. The left-hand side, however, would be s(90), which implies sine of some angle, which cannot be 0 at 90 degrees. Hence this angle proves the expression is not an identity.
• Angles 135 degrees and 270 degrees do not prove the expression incorrect in the same way as 90 degrees does.

Therefore, the correct answer is B. 90 degrees.