Problem 1011

Find a solution for the equation. Assume that all angles in which an unknown appears are acute angles.

cos (2α+30°) = sin(3α – 60°)

 

Solution:-

 

Since cos θ and sin θ are co-function, they are related by an identity.

The identity is cos θ = sin (90° – θ).

Thus, for acute angles, if a function and the co-function values are equal, the sum of the angles must be 90°.

2α + 30° + 3α – 60° = 90°

5α – 30° = 90°

5α = 120°

α = 24°

 

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