Question

if sin A =1/√10 and sin B =1/√5prove that A+B = 45​

Answer 1

Answer:

Step-by-step explanation:

sin A =1/√10 => Cos A= √1 - Sin²A = √1 - (1/√10)² = √9/10 = 3/√10.

sin B =1/√5 => Cos B = √1 - Sin²B = √1 - (1/√5)² = √4/5 = 2/√5.

Sin(A+B) = SinACosB+ CosASinB

              = 1/√10 * 2/√5 + 3/√10 * 1/√5

               = 3/√50 + 2/√50

              = 5/√50

              = 5/5√2

               = 1/√2

                = Sin 45°

=> A+B = 45°

Hence proved.