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

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

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)

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

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