Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Prove that:

sin squared straight A minus sin squared straight B space equals space sin left parenthesis straight A plus straight B right parenthesis. space sin left parenthesis straight A minus straight B right parenthesis

Answer

R.H.S. = sin(A+B). sin(A-B)
          = [sinA cosB + cosA sinB] [sinA cosB - cosA sinB]
          = sin squared straight A space cos squared straight B space minus space cos squared straight A space sin squared straight B
          = space space sin squared straight A left parenthesis 1 minus sin squared straight B right parenthesis minus space left parenthesis 1 minus sin squared straight A right parenthesis space sin squared straight B
          = sin squared straight A minus sin squared straight A space sin squared straight B minus sin squared straight B plus sin squared straight A space sin squared straight B
          = sin squared straight A minus sin squared straight B space equals space straight R. straight H. straight S.
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#6 {main}</pre>

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