How do you use the sum and difference formula to simplify #sin165#?

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How do you use the sum and difference formula to simplify #sin165#?

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Answer 1 · 2016-09-10T19:09:28

Use sin(135+30).

Explanation:

The sum formula for sin is #sin(A+B)=sinAcosB+cosAsinB#

Choose #A=135# and #B=30# because both of these values lie on the unit circle. From the unit circle:
#cos135=-sqrt2/2#
#sin135=sqrt2/2#
#cos30=sqrt3/2#
#sin30=1/2#

Let #A=135# and #B=30#
Substitute.
#sin(165)=sin(135+30)=sqrt2/2*sqrt3/2 + -sqrt2/2 * 1/2#

#sin(165)= sqrt6/4 -sqrt2/4#
#sin(165)=(sqrt6-sqrt2)/4#

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How do you use the sum and difference formula to simplify #sin165#?

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