Q. 273.9( 22 Votes )

If sin (A + B) = sin A cos B + cos A sin B , and

cos (A - B) = cos A cos B + sin A sin B, find the values of

(i) sin 75° and (ii) cos 15°.

Answer :

Given: sin (A + B) = sin A cos B + cos A sin B


cos (A - B) = cos A cos B + sin A sin B


(i) To find: sin 75°


If we put A = 30° and B = 45°, then we have:


sin 75° = sin 30° cos 45° + cos 30° sin 45°


sin 75° = (1/2) × (1/√2) + (√3/2) × (1/√2)


= (1/2√2) + (√3/2√2)


=


(ii) To find: cos 715°


If we put A = 45° and B = 30°, then we have:


cos 15° = cos 45° cos 30° + sin 45° sin 30°


cos 15° = (1/√2) × (√3/2) + (1/√2) × (1/2)


= (√3 / 2√2) + (1/2√2)


=


(i) sin 75° =


(ii) cos 15° =


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