show that sin 19 ° + sin 41 ° + sin 83 °= sin 23 ° + Sin 37 °+ sin 79 °

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Solution

RHS
sin23 + sin 37 + sin 79
=2 sin (37 +23) /2 x cos (37- 23)/2 + sin79
=2 sin 60/2 x cos 14/2 + sin (90-11)
=2 sin30 x cos 7 + cos 11
= 2 x 1/2 x cos (90 -83) + cos 11
= sin 83 + cos 11

LHS
sin 19 + sin41 + sin83
= sin (19 +41) + sin 83
= 2 sin (14+19) /2 x cos (41-19) /2 + sin 83
= 2 sin 60/2 x cos 22/2 + sin 83
=2 sin30 x cos 11 + sin 83
= 2 x 1/2 x cos 11 + sin 83
= cos 11 + sin 83

hence proved

like if satisfied

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