Question

How do you find the exact value of `sin70cos55-cos70sin55` using the sum and difference, double angle or half angle formulas?

Answer 1

`(sqrt2(sqrt3-1))/4`

Explanation:

`sin70cos55-cos70sin55= sin(70-55)=sin15=sin(45-30)=sin45*cos30-cos45*sin30=1/sqrt2*sqrt3/2-1/sqrt2*1/2= 1/(2sqrt2)(sqrt3-1)=(sqrt2(sqrt3-1))/4`[Ans]