Question

If tan theta+cot theta=5, then the value of tan^ theta+cot^2 theta is 1) 23 2) 25 3) 27 4) 15

Answer 1

tanθ+cotθ=5
Squaring both sides,
(tanθ+cotθ)²=25
or, tan²θ+2tanθcotθ+cot²θ=25
or, tan²θ+2tanθ(1/tanθ)+cot²θ=25
or, tan²θ+2+cot²θ=25
or, tan²θ+cot²θ=25-2
or, tan²θ+cot²θ=23
∴, The answer is 1)23