If Sin 3θ = Cos (θ – 6°) Where 3θ And θ − 6° Are Acute Angles, Find the Value of θ. - Mathematics

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If sin 3θ = cos (θ – 6°) where 3θ and θ − 6° are acute angles, find the value of θ.

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Solution

3θ, θ – 6 are an acute angle

We know that sin (90 – θ) = cos θ

sin 3θ = sin (90 – (θ - 6°))

sin 3θ = sin(90 – θ + 6°)

sin 3θ = sin (96° - θ)

3θ = 96° – θ

4θ = 96°

`θ = 96^@/4`

`θ = 24^@`

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Chapter 10: Trigonometric Ratios - Exercise 10.3 [Page 54]

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RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.3 | Q 15 | Page 54

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