How do you find the exact value of #sin30cos55-cos30sin55# using the sum and difference, double angle or half angle formulas?

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Answer 1 · 2016-09-22T02:42:07

Use #sin (a-b)=sin a cos b - cos a sin b and sin 3a = 3 sin a - 4

sin^3a#.

Using the first formula, the given expression reduces to

#s=-sin 25^o#

Using the second, this is related to #sin 75^o#:

#sin 75^o=sqrt2/4(1+sqrt3)=4s^3-3s#

Solving this cubic equation in s, the exact value of the given

expression s can be obtained, in a complicated form, as found in

.http://intmstat.com/blog/2011/06/exact-values-sin-degrees.pdf