SOLUTION: Evaluate the expression using trig identities. State the identity that you use. sin(pi/12)sin(5pi/12)

Question 383003: Evaluate the expression using trig identities. State the identity that you use.

sin(pi/12)sin(5pi/12)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Evaluate the expression using trig identities. State the identity that you use.
sin(pi/12)sin(5pi/12) ]
= sin(15 degrees)(sin(75 degrees)
= sin(45-30)*sin(45+30)
----
= [sin45cos30+cos45*sin30]
----
= [sin45cos30]^2 - [cos45sin30]^2
= [(sqrt(2)/2)(sqrt(3)/2)]^2 - [(sqrt(2)/2)(1/2)]^2
= [(sqrt(6)/4]^2 - [(sqrt(2)/4]^2
= 6/16 - 2/16
= 1/4
=====
Cheers,
Stan H.
RELATED QUESTIONS
Use the half-angle identity to evaluate the given expression exactly. (Enter the exact... (answered by lwsshak3)

find the quotient 3(cos 5pi/12 + i sin 5pi/12) divided by 6(cos pi/12 + i sin... (answered by jim_thompson5910)

sin... (answered by jsmallt9)

Use an identity to find the exact value of the expression sin(pi/4 +... (answered by lwsshak3)

Evaluate the expression without using a calculator (sin pi/6 cos pi/4 - sin pi/4 cos... (answered by lwsshak3)

Suppose a genius figured out that sin(7pi/12)= -((sqrt(2)+sqrt(60)/4) Find each of (answered by KMST)

use an appropriate identity to find the exact value of the expression cos... (answered by stanbon,josgarithmetic)

I have to solve this function: f(-�/4)= cos2x *let �= pi So far I have gotten this... (answered by solver91311)

If sin(theta)= (sqrt2)/5, and pi/2 < theta < pi, then find the exact value of tan(2theta) (answered by lwsshak3)