Question

If sin (x+y) = cos(x-y) find the value of x

Answer 1

==> sin(x + y) = cos( x - y)

==> sin(x + y) = sin(90 - (x - y))

{ sin(90 - θ) = cos θ }

==> x + y = 90 - (x - y)

==> x + y = 90 - x + y

==> x = 90 - x

==> 2x = 90

==> x = 45

Hence, Value of x is 45°

Answer 2

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

sin (x+y) = sin(90-(x-y))

" sin (90-A) = cos (A) "

(x+y) = 90-(x-y)

(x+y) = 90- x+y

x = 90-x

2x = 90

x = 90/2

x = 45

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