Question

For what value of theta, cot 3theta cot(30° + theta)​

Answer 1

We have:

$\cot 3\theta$ = $\cot (30+\theta)$

We have to find, the value of $\theta.$

Solution:

∴ $\cot 3\theta$ = $\cot (30+\theta)$

⇒ 3$\theta$ = 30° + $\theta$

⇒  3$\theta$ -  $\theta$ = 30°

⇒ 2$\theta$  = 30°

⇒ $\theta$  = $\dfrac{30}{2}$

⇒ $\theta$  = 15°

∴ $\theta$  = 15°

Thus, the value of $\theta$  is equal to 15°.

Answer 2

Given  : Cot 3θ  = Cot(30° + θ)

cot 3theta cot(30° + theta)​

To Find : θ

Solution:

Cot 3θ  = Cot(30° + θ)

cot has period of π  = 180°

 3θ  = 30° + θ  ± n(180°)

=> 2θ = 30°   + n(180°)

=> θ = 15°    ± n(90°)

θ = 15°    ±  n(90°)

value of theta = 15°    ±  n(90°)

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