Question

If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to ______.

Options

• 9°

• 30°

• 27°

• 45°

Answer 1

If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to 27°.

Explanation:

We have, cos(81° + θ) = `sin(k/3 - θ)`

`\implies  81^circ + θ + k/3 - θ` = 90°  ...[∵ cos α = sin β, then α + β = 90°]

`\implies k/3` = 90° – 81°

`\implies` k = 27°