Principle of Mathematical Induction

Principle of Mathematical Induction

Question

In ∆ABC, prove that:

space space space cos space left parenthesis straight A plus straight B right parenthesis plus cos space straight C space equals space 0

Answer

In increment ABC comma
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∴        cos left parenthesis straight A plus straight B right parenthesis space equals space cos left parenthesis 180 degree minus straight C right parenthesis space equals space cos left parenthesis straight pi minus straight C right parenthesis
space space straight pi minus straight C  is in quadrant II, means cos left parenthesis straight pi minus straight C right parenthesis is -ve
∴                     cos (A + B) = - cos C
Hence,   cos (A + B) + cos C = 

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