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Question
If A = B = 45°, verify that sin (A - B) = sin A .cos B - cos A.sin B
Solution
A = B= 45°
L.H.S.
= sin(A - B)
= sin(45° - 45°)
= sin0°
= 0
R.H.S.
= sinA cosB - cosA sinB
= sin45° x cos45° - cos45° x sin45°
= `(1)/sqrt(2) xx (1)/sqrt(2) - (1)/sqrt(2) xx (1)/sqrt(2)`
= `(1)/(2) - (1)/(2)`
= 0
⇒ sin(A - B) = sinA cosB - cosA sinB.
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