I M Having Trouble Solving This Trig Problem 1 1 Tan 2x 1 1 Cot 2x 1 Any He

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

Solution

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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