Question

if tan theta + cot theta= 2
find tan^4 theta + tan^2 theta​

Answer 1

Answer:

tan^4 theta + tan^2 theta​ =2

Step-by-step explanation:

$let \ tan\theta \ = \ t\\t + 1/t =2\\t^2 + 1 =2t\\t^2 - 2t +1=0\\(t-1)^2=0\\t=1\\tan\theta =1\\(tan\theta)^4 + (tan\theta)^2=\\=1+1\\=2$

Answer 2

Answer is: 5/16

Step-by-step explanation:

$tan\theta+cot\theta=2\\tan\theta+(1/tan\theta)=2\\tan^{2}\theta+1=2tan\theta\\tan^{2}\theta-2tan\theta+1=0\\(tan\theta-1)^{2}=0\\(tan\theta-1)=0\\tan\theta=1\\tan\theta=tan45\degree\\\theta=45 \\\\------------------------------------------------------\\\\tan^{4}\theta+tan^{2}\theta\\=tan^{4}45+tan^{2}45\\=(1/2)^{4}+(1/2)^{2}\\=1/16+1/4\\=5/16$