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sin 78 degree-sin66degre-sin 42degree+sin6degree
Asked by amitras0003 | 26 Jan, 2024, 06:53: AM
answered-by-expert Expert Answer

let x = sin78° - sin42° - sin66° + sin6°

= sin(60+18)° - sin(60-18)° - sin(36+30)+sin(36-30)

Let us use the trignometry identity " sin(A+B) - sin(A-B) = 2 cosA sinB "

= 2 cos60° sin18° -  2 cos36° sin30°

= sin18° - cos36°

=sin18° - (1 - 2 sin218) = 2 sin218 + sin18° - 1 = -0.5

 

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