At what angle θ, the value of sin(θ) and cos(θ) will have the same value?

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Accepted Answer

We need to find the angle θ for which sin(θ) = cos(θ).

Recall the trigonometric identity: sin(θ) = cos(90° - θ).

For sin(θ) = cos(θ), this implies:

sin(θ) = cos(θ)
=> sin(θ) = sin(90° - θ)

This equality holds when θ = 90° - θ
=> 2θ = 90°
=> θ = 45°

Therefore, sin(45°) = cos(45°) = √2/2.

Hence, the correct answer is 45°.

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