given that Sin A + B equal to sin a cos b + cos a sin b find the value of sin 75 degree
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Sol: Given Sin(A+B) = Sin A Cos B + Cos A Sin B. Sin 75 = Sin ( 45 + 30) = Sin 45 Cos 30 + Cos 45 Sin 30. Sin 75 = (1 / √2) ( √3 / 2) + (1 / √2) ( 1 / 2) = [ √3 + 1] / 2√2.
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Sin 75 = Sin (30 + 45)
= Sin 30 Cos 45 + Sin 45 Cos 30
= (1 / 2) (1 / root2) + (1 / root2) (root3 / 2)
= (1 / 2 root2) + (root 3 / 2 root2)
= (1 + root3) / 2 root2
On rationalising :-
(1 + root3) (2 root2) / (2 root2) (2 root2)
(2 root2 + 2 root6) / 8
2 (root2 + root6) / 8
(root2 + root6) / 4
Therefore Sin75 = (root2 + root6) / 4
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