Use the cofunction identities to evaluate the expression without using a calculator.
Sin²25° + sin²65°

Question

Use the cofunction identities to evaluate the expression without using a calculator. Sin²25° + sin²65° A)-1 B)-2 C)1 D)2 E)3

Quizplus · Accepted Answer

We can use the cofunction identities:

sin(90° - x) = cos(x) and sin(90° + x) = cos(x)

To write the expression as:

cos(25°) + cos(25°)

We know that the cosine function is an even function, which means that:

cos(-x) = cos(x)

Therefore, we can write:

cos(25°) = cos(-25°)

And the expression becomes:

cos(-25°) + cos(25°)

Adding these two cosine values together gives:

cos(-25°) + cos(25°) = 2 cos(25°)

And we know that cos(25°) is approximately equal to 0.9063.

Therefore, 2 cos(25°) is approximately equal to 1.8126, which rounds to 1.

So the answer is C) 1.

Use the Cofunction Identities to Evaluate the Expression Without Using