Question

Tan 2 theta - 10 cot 2 theta=3

Answer 1

We know, cot 2θ = 1/tan 2θ

Multiplying tan 2θ both side of the given equation.

tan²2θ - 3tan 2θ - 10 = 0

tan²2θ - 5tan 2θ + 2tan 2θ - 10 = 0

tan 2θ ( tan 2θ - 5 ) + 2 ( tan 2θ - 5 ) = 0

tan 2θ = -2 or tan 2θ = 5

Therefore,
`\theta = (tan^(-1) (-2))/(2)` or
`\theta = (tan^(-1) (5))/(2)`

Hence, this is the required solution.