Question

solve for x : tan^2 (x) + cot^2(x) = 2

Answer 1

x=45degree.
hopefully it helps you

Answer 2

2=(tan²x+cot²x)
(tan²x+1/tan²x)=2
tan⁴x+1=2tan²x
tan⁴x-2tan²x+1=0
tan⁴x-tan²x-tan²x+1=0
tan²x(tan²x-1)-1(tan²x-1)=0
(tan²x-1)(tan²x-1)=0
tan²x-1=0
tan²x=1
tanx=√1
tanx=±1
tanx=1
tanx=tanπ/4
x=π/4
tanx=-1
tanx=-tanπ/4=tan3π/4
x=3π/4