Question

3sinA + 4cosA = 5 then prove that sinA = 3/5​

Answer 1

Step-by-step explanation:

3/5 Sin A + 4/5 Cos A = 1

we see that (3/5)² + (4/5)² = 1

let 3/5 = Sin B and 4/5 = Cos B

So Sin A Sin B + Cos A Cos B = 1 = Cos 0°

Cos (A - B) = cos 0°

A = B or A - B = 2 π

if A = B, Sin A = Sin B = 3/5.

or, if A - B = 2π, Sin A = Sin (2π+B) = Sin B = 3/5

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alternately:

4 Cos A = 5 - 3 Sin A

16 Cos² A = 25 + 9 Sin² A - 30 Sin A

16 - 16 Sin² A = 25 + 9 Sin² A - 30 Sin A

25 Sin² A - 30 Sin A + 9 = 0

Sin A = [ 30 +- √(900 - 900) ] / 50 = 3/5