optinal maths question
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Given,
sin A = 1/√10 and sin B = 1/√5
We know that sin2x + cos2x = 1
Thus, cos A = √(1 – sin2A) = 3/√10
cos B = √(1 – sin2B) = 2/√5
As we know,
sin(A + B) = sin A cos B + cos A sin B
= (1/√10) (2/√5) + (3/√10) (1/√5)
= (2 + 3)/√50
= 5/(5√2)
= 1/√2
sin (A + B) = sin π/4 {since A and B are acute angles as per the given}
Therefore, A + B = π/4
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