Use the figure to find the exact value of the following trig

Use the figure to find the exact value of the following trigonometric function. cos alpha/2 cos alpha/2 = 1. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

We have given opposite side=8 and adjacent side=15 from right triangle

hypotenuse =sqrt(64+225)=sqrt(289)=17

cos()=15/17 =adjacent side/hypotenuse

we know that cos(/2)=sqrt((1+cos())/2)

substitute cos() into cos(/2)

cos(/2)=sqrt((1+(15/17))/2)

cos(/2)=sqrt(32/34)=sqrt(16/17)

cos(/2)=sqrt(16/17)