How do you prove #sin 5pi/12 = sin pi/6 cos pi/4 + cos pi/6 sin pi/4#?

Question

Mathematics

Bryan Williams

4 May, 22:50

How do you prove #sin 5pi/12 = sin pi/6 cos pi/4 + cos pi/6 sin pi/4#?

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Answers (1)

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Abigayle Hodge · Answer 1

You rewrite 5π/12 as 2π/12 + 3π/12 since 2 + 3 = 5.

Then you simplify the fractions into π/6 + π/4.

Then you use the sine addition identity.

sin (5π/12) = sin (π/6 + π/4) = sin π/6 cos π/4 + cos π/6 sin π/4