Principle of Mathematical Induction

Principle of Mathematical Induction

Question

If tan open parentheses straight x over 2 close parentheses space equals space 3 over 4 comma find the value of:

sin space straight x

Answer

We know that
          sin space 2 straight A space equals space fraction numerator 2 space tanA over denominator 1 plus tan squared straight A end fraction
Replacing A byspace space straight x over 2 comma we get
                          sinx space equals space fraction numerator 2 tan open parentheses begin display style straight x over 2 end style close parentheses over denominator 1 plus tan squared open parentheses begin display style straight x over 2 end style close parentheses end fraction space equals space fraction numerator 2 open parentheses begin display style 3 over 4 end style close parentheses over denominator 1 plus open parentheses begin display style 3 over 4 end style close parentheses squared end fraction space equals space 3 over 2 cross times 16 over 25 equals space 24 over 25
Hence,                 sinx space equals space 24 over 25

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