Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the value of:

sin open parentheses straight pi over 12 close parentheses

Answer
sin open parentheses straight pi over 12 close parentheses space equals space sin open parentheses 180 over 12 close parentheses to the power of degree space equals space sin space 15 degree space equals space sin left parenthesis 45 degree minus 30 degree right parenthesis
               equals sin 45 degree cos 30 degree minus cos 45 degree sin 30 degree

               equals fraction numerator 1 over denominator square root of 2 end fraction space cross times space fraction numerator square root of 3 over denominator 2 end fraction minus fraction numerator 1 over denominator square root of 2 end fraction cross times 1 half space equals space fraction numerator 1 over denominator 2 square root of 2 end fraction left parenthesis square root of 3 minus 1 right parenthesis
Hence,    sin open parentheses straight pi over 12 close parentheses space equals space fraction numerator square root of 3 minus 1 over denominator 2 square root of 2 end fraction

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