Question

Find the angle θ in the following, if 0° < θ < 90°.

sin (2θ − 10°) = cos (θ + 40°)

Answer 1

cos x = sin (90∘ − x)

sin (2θ − 10°) = cos (θ + 40°)

Step 1:

Replace cos⁡ (θ + 40°) with sin ⁡[90° − (θ + 40°)] = sin (50° − θ)

sin (2θ − 10°) = sin(50° − θ)

For 0° < θ < 90°,

Step 2:

For  0° < θ < 90°, two cases are possible:

Case 1:

2θ − 10° = 50° − θ

3θ = 60°

θ = 20°

Case 2:

2θ − 10° = 180° − (50° − θ)

2θ − 10° = 130° + θ

θ = 140°(invalid since θ < 90°)

So Answer is 20°