# Solve: `sin^2x = cos^2x`

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### 2 Answers

Take the square root of both sides.

`sin x = cos x`

Then, refer to Unit Cirle Chart to determine the angle that resulted to same values of sine and cosine function.

Base on it, the `theta` that makes the angle sine and cosine equal are `pi/4 , and (5pi)/4` .

Since there is no indicated interval for the value of the angle, the general solution is:

>> `theta_1 = pi/4 + 2pi k` ** and** `theta_2 = (5pi)/4 + 2pi k` **(Answer)**

The equation `sin^2x = cos^2x` has to be solved.

`sin^2x = cos^2x`

=> `tan^2x = 1`

=> tan x = 1 and tan x = -1

=> x = `tan^-1(1)` and x = `tan^-1(-1)`

=> x = 45 degrees and x = -45

**The general solution of the equation is 45 + n*180 and -45 + n*180 degrees.**