Question

Find tetha?
IF 3tan tetha= cot tetha​

Answer 1

3tanθ + cotθ = 5cosecθ

as you know,

tanθ = sinθ/cosθ , cotθ = cosθ/sinθ and cosecθ = 1/sinθ use it here,

⇒3tanθ + cotθ = 5cosecθ

⇒3sinθ/cosθ + cosθ/sinθ = 5/sinθ

⇒(3sin²θ + cos²θ)/sinθ.cosθ = 5/sinθ

⇒3sin²θ + cos²θ = 5cosθ

We know, sin²θ = 1 - cos²θ use it here,

⇒3(1 - cos²θ) + cos²θ - 5cosθ = 0

⇒3 - 3cos²θ + cos²θ - 5cosθ = 0

⇒2cos²θ + 5cosθ - 3 = 0

⇒2cos²θ + 6cosθ - cosθ - 3 = 0

⇒2cosθ(cosθ + 3) - (cosθ+ 3) = 0

⇒(2cosθ - 1)(cosθ + 3) = 0

⇒cosθ = 1/2 and -3 but cosθ∈[ -1, 1 ] so, cosθ ≠ -3

Hence, cosθ = 1/2 = cosπ/3

θ = 2nπ ± π/3 [ by using general solution of trigonometric ]

Answer 2

Step-by-step explanation:

i hope it helps you.....

a is your option