Question

What is the value of x? `sin(x+21^@)=cos(2x+21^@)`

Answer 1

Given: `sin(x+21^@)=cos(2x+21^@)`

Use the identity `cos(90^@-theta) = sin(theta)` where `theta = x+21^@`

`cos(90^@-x-21^@)=cos(2x+21^@)`

Simplify the left:

`cos(69^@-x)=cos(2x+21^@)`

Use the inverse cosine on both sides:

`69^@-x=2x+21^@`

`3x = 48^@`

`x = 16^@ larr` This is first value to the right of 0; there is an infinite number to the left and to the right of 0.