Question

write the following expression as the sine, cosine, or tangent of a double angle. then find the exact value of the expression.
2 sin 157.5° cos 157.5°
write the following expression as the sine, cosine, or tangent of a double angle. select the correct choice below and fill in the answer box to complete your choice.
(simplify your answer. type your answer in degrees. use integers or decimals for any numbers in the expression.)
○ a. 2 sin 157.5° cos 157.5° = sin□°
○ b. 2 sin 157.5° cos 157.5° = cos□°
○ c. 2 sin 157.5° cos 157.5° = tan□°

Explanation:

Step1: Use double - angle formula for sine

The double - angle formula for sine is \(\sin(2\alpha)=2\sin\alpha\cos\alpha\).
Here \(\alpha = 157.5^{\circ}\), so \(2\sin157.5^{\circ}\cos157.5^{\circ}=\sin(2\times157.5^{\circ})\).

Step2: Calculate the value of the double - angle

\(2\times157.5^{\circ}=315^{\circ}\)

Answer:

A. \(2\sin157.5^{\circ}\cos157.5^{\circ}=\sin315^{\circ}\)