Use the cofunction identities to evaluate the expression without the aid of a calculator.sin2 53° + sin2 37°

Sure, let's use the cofunction identities to evaluate the expression sin^2 53° + sin^2 37°.

Step 1: Recognize the cofunction identity The cofunction identity for sine and cosine is sin(90° - θ) = cos(θ). This means that sin(53°) = cos(37°) and sin(37°) = cos(53°).

Step 2: Apply the cofunction identity We can rewrite the expression sin^2 53° + sin^2 37° as cos^2 37° + cos^2 53°.

Step 3: Use the Pythagorean identity The Pythagorean identity for cosine is cos^2 θ + sin^2 θ = 1. This means that cos^2 37° + sin^2 37° = 1 and cos^2 53° + sin^2 53° = 1.

Step 4: Substitute the Pythagorean identity We can substitute the Pythagorean identity into our expression to get 1 + 1 = 2.

So, sin^2 53° + sin^2 37° = 2.