Question

Find a solution for the equation. Assume that all angles are acute angles.

sec θ = csc(θ + 32°)

Answer 1

Re-write the left side as 1/cos(θ) and right side as 1/sin(θ + 32°).
Now note that cos(θ) = sin(90° - θ). Now we re-write the equation as:

1/sin(90° - θ) = 1/sin(θ + 32°).

This implies that 90° - θ = θ + 32°. Re-arranging gives:

=> 2θ = 58° => θ = 29°

Answer 2

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