The value of cos57+sin27 is
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Answer: cos 3°
Step-by-step explanation:
= cos 57 - cos ( 90 - 27) ...........( sin A = cos (90-A)
= cos 57 - cos 63
applying cos C + cos D = 2cos (C+D/2) cos ( C-D/2)
= 2 cos (57 + 63 / 2) cos ( 57 - 63 / 2)
= 2 cos ( 120 / 2 ) cos (-6/2)
= 2 cos (60) cos ( - 3)
= 2 cos 60 cos 3 .............( cos ( - A) = cos A )
= 2 x 1/2 x cos 3°
= cos 3°
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