Question

If theta is a positive acute angle and tan 3 theta = cot(60- theta), find the value of sin 3 theta

Answer 1

Answer:

Step-by-step explanation:

Given:

tan2θ tan3θ = 1

Concept used:

1/tanθ = cotθ  

cotθ = tan(90o - θ )

Calculation:

tan2θ tan3θ = 1

⇒ tan3θ = 1/tan2θ  

⇒ tan3θ = cot2θ  

⇒ tan3θ = tan(90o - 2θ)  

⇒ 3θ = 90 - 2θ  

⇒ 5θ = 90o

⇒ θ = 18o

Hence, The value of θ is 18o.