Question

If tanθ + cotθ = 5 then the value of

tan2θ + cot2θ is ____.....​

Answer 1

==> tan θ + cot θ = 5

Square both sides,

==> ( tan θ + cot θ )² = 5²

==> tan² θ + cot² θ + 2 tan θ × cot θ = 25

==> tan² θ + cot² θ + 2 × tan θ × 1 / tan θ = 25 ( °•° cot θ = 1 / tan θ )

==> tan² θ + cot² θ + 2 = 25

==> tan² θ + cot² θ = 25 - 2

==> tan² θ + cot² θ = 23