Question

if tan teeta +cot teeta =2 find tge value of tan^2teeta+ cot^2teeta

Answer 1

Given,
tan θ + cot θ = 2

Squaring on both sides,
(tan θ + cot θ )² = 2²
tan²θ + cot²θ + 2(tanθ)(cotθ) = 4
tan²θ + cot²θ + 2(tanθ)(1/tanθ) = 4
tan²θ + cot²θ + 2 = 4
tan²θ + cot²θ = 4 - 2
tan²θ + cot²θ = 2

Hope it helps

Answer 2

Given,

tanθ+cotθ=2

REQUIRED TO FIND :- tan²θ+cot²θ=

Formulae :-

1) a² + b²= ( a+ b)² - 2 ab.

2) tan θ. cot θ = 1

Process :-

tan²θ+cot² θ

=(tanθ+cotθ)²-2tanθcotθ

=2²-2

=4-2

=2

hope helped !!