Principle Of Mathematical Induction

Question
CBSEENMA11014311

Prove that:

sin open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 minus cosx over denominator 2 end fraction end root

Solution

We know that:
                cos space 2 straight A space equals space 1 minus 2 sin squared straight A
Replacing A by space space straight x over 2 comma  we get
                       cosx space equals space 1 minus 2 sin squared open parentheses straight x over 2 close parentheses                            rightwards double arrow         2 sin squared open parentheses straight x over 2 close parentheses space equals space 1 minus cosx
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#6 {main}</pre>                              rightwards double arrow         sin open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 minus cosx over denominator 2 end fraction end root

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