Question

Find the value of θ from the following equation.(θ≤90°)​

Answer 1

Answer: 10°

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We are given:

Sin(6θ) = Cos(3θ)

Solving for θ:

Simplifying Cos(3θ):

We know that:

Cos(θ) = Sin(90-θ)

So, we can say that:

Cos(3θ) = Sin(90 - 3θ)

Finding the value of θ:

Sin(6θ) = Cos(3θ)

Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]

6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]

9θ = 90 [adding 3θ on both sides]

θ = 10° [dividing both sides by 9]