Question
If sin (4A − 5B) = (√2/2) and cos (A + B) = (√2/2),
where 0° < A, B < 90°, then find the value of ‘A’.Solution
sin (4A − 5B) = (√2/2)
Or, sin (4A − 5B) = sin 45°
Or, 4A − 5B = 45° ----------- (I)
And, cos (A + B) = (√2/2)
Or, cos (A + B) = cos 45°
Or, A + B = 45° -------------- (II)
On solving equation I + 5 × equation II, we get;
4A − 5B + 5 × (A + B) = 45 + 5 × 45
Or, 4A − 5B + 5A + 5B = 270°
Or, 9A = 270°
So, ‘A’ = 30°
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