I'm having trouble solving this trig problem: 1/1+tan^2x + 1/1+cot^2x = 1..any help?

Question

I tried looking it up, but I can't use any new trig identities for my problem, I can only use:

tanx= sinx/cosx

secx=1/cosx

cotx=cosx/sinx

cscx=1/sinx

Answer 1

1+ tan²x= 1+sin²x/cos²x

Find common denominator which is cos²x

cos²x/cos²x + sin²x/cos²x

(cos²x + sin²x)/cos²x

1+cot²x = 1+ cos²x/sin²x

Common denominator is sin²x

sin²x/sin²x + cos²x/sin²x

( sin²x + cos²x)/sin²x

1/(cosx²+ sin²x)/cos²x + 1/( sin²x + cos²x)/sin²x

Multiply the numerator and denominator by the reciprocal of the bottom fractions to get

cos²x/(cosx²+ sin²x )+ sin²x/( cosx²+ sin²x)

Since they now have common denominator you can add the tips

(cosx²+ sin²x)/(cosx²+ sin²x)

1/1 = 1