Question

How do you solve `sin x = cos (x + 50)`?

Answer 1

Solve sin x = cos (x + 50)

Ans: `x = 20^@`

Explanation:

Apply the trig identity: `cos x = sin (pi/2 - x)`, we get
sin x = cos (x + 50) = sin (90 - x - 50) = sin (40 - x)
`x = 40 - x` --> `2x = 40` --> `x = 40/2 = 20^@`

Check by calculator.
x = 20 --> sin x = 0.34 --> cos (x + 50) = cos 70 = 0.34. OK