Question

If tan θ+ cot θ=2,find the value of tan²θ+ cot² θ

Answer 1

Theta is written as A,




tanA + cotA = 2


Square on both sides,




( tanA + cot A )² = 2²

tan²A + cot²A + 2 tanA cotA = 4

tan²A + cot²A + 2( tanA × 1 / tanA ) = 4

tan²A + cot²A + 2( 1 ) = 4

tan²A + cot²A + 2 = 4

tan²A + cot²A = 4 - 2

tan²A + cot²A = 2

$..$

Answer 2

Tan theta + cot theta =2
(Tan theta + cot theta)^2=4
Tan^2theta + cot^theta +2tanthetacottheta =4
Since tan theta=1/cot theta,tan theta and cot theta gets cancelled in 2tan theta ×cot theta,leaving only 2.
Tan^2theta + cot^theta +2=4
So Tan^2thet + cot^2theta=2