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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