Question

14. If sin 3 thetha = cos (thetha - 6°), where 3thetha and thetha - 6° are both acute angles, find the value of thetha.​

Answer 1

Answer :

θ = 24°

Solution :

• Given : sin3θ = cos(θ - 6°)
• To find : θ = ?

We know that sine and cosine are complements of each other , ie ;

• sin∅ = cos(90° - ∅)

• cos∅ = sin(90° - ∅)

Thus ,

=> sin3θ = cos(θ - 6°)

=> sin3θ = sin[90° - (θ - 6°)]

=> 3θ = 90° - (θ - 6°)

=> 3θ = 90° - θ + 6°

=> 3θ + θ = 90° + 6°

=> 4θ = 96°

=> θ = 96°/4

=> θ = 24°

Hence θ = 24° .