Q. 143.9( 9 Votes )
If A = 60° and B = 30°, verify that:
(i) sin (A + B) = sin A cos B + cos A sin B
(ii) cos (A + B) = cos A cos B — sin A sin B
Answer :
(i) To verify: sin (A + B) = sin A cos B + cos A sin B
If A = 60° and B = 30°, then
To verify: sin 90° = sin 60° cos 30° + cos 60° sin 30°
Consider R.H.S. = sin 60° cos 30° + cos 60° sin 30°
= (√3/2) × (√3/2) + (1/2)(1/2)
= (3/4) + (1/4)
= 4/4
=1
Consider L.H.S. = sin 90° = 1
∴ L.H.S. = R.H.S.
Hence, verified.
(ii) To verify: cos (A + B) = cos A cos B — sin A sin B
If A = 60° and B = 30°, then
To verify: cos (90°) = cos 60° cos 30° — sin60° sin 30°
Consider R.H.S. = cos 60° cos 30° - sin 60° sin 30°
= (1/2) × (√3/2) - (√3/2)(1/2)
= (√3/4) - (√3/4)
= 0 = cos 90° = L.H.S.
∴ L.H.S. = R.H.S.
Hence, verified.
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