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Question
If A = B = 45°, verify that cos (A − B) = cos A. cos B + sin A. sin B
Solution
A = B = 45°
L.H.S.
= cos (A − B)
= cos (45° − 45°)
= cos 0°
= 1
R.H.S.
= cos A cos B + sin A sin B
= cos 45° x cos 45° + sin 45° x sin 45°
= `(1)/sqrt(2) xx (1)/sqrt(2) + (1)/sqrt(2) xx (1)/sqrt(2)`
= `(1)/(2) + (1)/(2)`
= 1
⇒ cos (A − B) = cos A cos B + sin A sin B
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