Write the following expression as the sine cosine or tangent

Write the following expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 2 sin 67.5 degree The expression written as the sine, cosine, or tangent of a double angle is degree. (Type any angle measures in degrees.)

Solution

We have given 2sin(67.5⁰)*cos(67.5⁰)

we know the sin(2*theta)=2sin(theta)cos(theta)

2sin(67.5⁰)*cos(67.5⁰)=sin(2*67.5⁰)=sin(135⁰)

the expression written as sine of double angle is 135⁰

sin(135⁰)=1/sqrt(2)