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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