Question
If sin (2x + 50) o = cos (2y -
50) o, such that, 0o < x + y < 90o, then find the value of tan(x + y) .Solution
Sin (2x + 50) o = cos(2y - 50) o
We know that, sin Ao = cos (90 - A) o
Or, cos {90o - (2x + 50) o} = cos(2y - 50) o
Or, 90 - (2x + 50) = 2y - 50
Or, 90 - 2x - 50 = 2y - 50
Or, 2x + 2y = 90
Or, 2 X (x + y) = 90
So, x + y = (90/2) = 45o
Therefore, tan (x + y) = tan 45o = 1
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