Question

if sin ( A+B) = sin A cos B + cos A sin B. then find the value of sin 75°​

Answer 1

Answer: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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Answer 2

Answer:

$given \: \sin(75)$

sin(A+B)=sinAcosB+cosAsinB

$\sin(75 ) = \sin(45 + 30) \\ = \sin(45) \cos(30) + \cos(45) \sin(30) \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ = \frac{ \sqrt{3 } + 1 }{2 \sqrt{2} } \: here \: is \: your \: answer$

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