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prove that (sin239-sin221)(sin257-sin23)=3/16:-

prove that (sin239-sin221)(sin257-sin23)=3/16:-

Grade:

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
6 years ago
Solution:
We have:
sin(239)-sin(221)=2cos(230)sin(9) and sin(257)-sin(23)=2cos(140)sin(117)
So,
we get:
(sin(239)-sin(221))*(sin(257)-sin(23)) =4cos(230)sin(9)cos(140)sin(117) =-\left (2sin(140)cos\left (140 \right ) \right )\left (2cos\left (27 \right )cos\left (81 \right ) \right ) =-sin(280)\left (cos(108)+cos(54) \right ) =sin(80)sin(18)-sin(80)sin(36) =sin(80)(sin(18)-2sin(18)cos(18)) =sin(18)cos(10)(1-2cos(18))Regards
Sumit

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