Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Show that: sin space 51 degree space plus space cos space 81 degree space equals space cos space 21 degree

Answer

L.H.S. = sin space 51 degree space plus space cos space 81 degree space equals space sin space 51 degree space plus space cos left parenthesis 90 degree space minus space 9 degree right parenthesis space equals space sin space 51 degree space plus space sin space 9 degree
          = 2 sin open parentheses fraction numerator 51 degree plus 9 degree over denominator 2 end fraction close parentheses. space cos open parentheses fraction numerator 51 degree minus 9 degree over denominator 2 end fraction close parentheses space equals space 2 space sin 30 degree space cos space 21 degree
          = 2 space cross times space 1 half space cross times space cos space 21 degree space equals space cos space 21 degree space equals space straight R. straight H. straight S.
Hence,    L.H.S. = R.H.S.

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