Question

If tan^2 theta + cot^2 theta = 66/25 find the value of tan theta - cot theta​

Answer 1

tan²θ + cot²θ =   $\frac{66}{25}$

(tanθ + cotθ) (tanθ - cotθ) =  $\frac{66}{25}$

(tanθ - cotθ) =   $\frac{66}{25}$ × 1/ (tanθ + cotθ)

(tanθ - cotθ) =  $\frac{66}{25}$ × 1/ (sinθ/cosθ + cosθ/sinθ)

(tanθ - cotθ) =   $\frac{66}{25}$ × 1 / (sin²θ + cos²θ/ sinθ cosθ)

(tanθ - cotθ) =   $\frac{66}{25}$ × 1 / (1/ sinθ cosθ)

(tanθ - cotθ) =   $\frac{66}{25}$ × 1 × sinθ cosθ

(tanθ - cotθ) =   $\frac{66}{25}$  × sinθ cosθ

hope it helps u

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