Question

If is 3sinx+4cosx=5 then proved that, sinx=3/5

Answer 1

3sin(x) + 4cos(x) = 5
(3/5)sin x + (4/5) cos x = 1

put (3/5) = cos y and (4/5) = sin y, because sin^2 y +cos^2 y = 16/25+9/25=25/25=1
sin x(cos y) +cos x (sin y) = 1
sin (x+y) = 1 = sin 90
x + y = 90 or pi/2
x = (90- y) or x = (pi/2 - y)
therefore sin x = cos y = 3/5...............................Ans
Hence proved

Answer 2

Answer:

Step-by-step explanation:

3sin(x) + 4cos(x) = 5

(3/5)sin x + (4/5) cos x = 1

put (3/5) = cos y and (4/5) = sin y, because sin^2 y +cos^2 y = 16/25+9/25=25/25=1

sin x(cos y) +cos x (sin y) = 1

sin (x+y) = 1 = sin 90

x + y = 90 or pi/2

x = (90- y) or x = (pi/2 - y)

therefore sin x = cos y = 3/5.