Question

if sin (A+B)=sin A cos B+cos A sin B then find the value of sin 75° & cos 15°

Answer 1

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Answer 2

Hey !!!

If sin (A + B ) = sinA *cosB + cosA *sinB

We can write sin75° = sin ( 30° + 45° ) similarly

hence , sin(30° + 45° ) = sin30° ×cos45° + cos30° ×sin45°

=> 1/2 × 1/√2 + 1/2 ×1/√2 [putting value of each identity]

=> 1/2*1/√2 + √3/2*1/√2

=> 1/2√2 + √3/2√2

=> 1 + √3
---------------- Answer ✔
2√2 .

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2nd ,

cos15° = cos ( 45° - 30° )

•°• cos ( A - B ) = cosA ×cosB + sinA ×sinB

hence , cos15 ° = cos (45 ° - 30° )

= cos45° ×cos30° + sin45° × sin30°

= 1/√2 × √3/2 + 1/√2× 1/2

= √3 + 1
---------------
2 √2

hence , here sin75° = cos15° = √3 + 1 /2√2

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Hope it helps you !!

@Rajukumar111