Question

Solve the equation: tan^2x+cot^2x=2​

Answer 1

45 degrees

Explanation:

Convert both tan and cot to sin and cos:

Let theta = x (because I can't put theta here)

`tan^(2) x + cot^(2)x = 2\\(sin^(2) )/(cos^(2) ) + (cos^(2) )/(sin^(2) ) =2\\(sin^(4)x + cos^(4)x )/(cos^(2)xsin^(2)x  )  =2 \\sin^(4)x + cos^(4)x = 2cos^(2)xsin^(2)x\\sin^(4)x + cos^(4)x - 2cos^(2)xsin^(2)x =0 \\sin^(4)x  - 2cos^(2)xsin^(2)x + cos^(4)x = 0\\(sin^(2)x - cos^(2)x)^(2)  =0\\sin^(2)x - cos^(2)x =0\\sin^(2)x = cos^(2)x \\(sin^(2)x)/(cos^(2)x)  = 1\\tan^(2)x = 1\\x = 45 degrees`

Answer 2

Good evening ,

___________________

Explanation:

Look at the photo below for the detailed answer.

:)