Question

Prove that sinƟ= cos (90)​

Answer 1

To prove that sinθ = cos(90°), we can use the fact that the cosine function is the sine function shifted by 90 degrees. In other words, cosθ = sin(90° - θ).

Therefore, cos(90°) = sin(90° - 90°) = sin(0°)

Since the sine function is defined as the ratio of the opposite side to the hypotenuse of a right triangle, and the angle 0° corresponds to a triangle with an opposite side of 0, we know that sin(0°) = 0.

Hence, cos(90°) = sin(0°) = 0.

Therefore, sinθ = cos(90°) is true when θ = 0°, and more generally, for any angle θ, sinθ = cos(90° - θ).

Answer 2

To prove the equation sinθ = cos(90°), we can use the fact that the cosine function is equal to the sine function shifted by 90 degrees. By applying trigonometric identities and simplifying, we can show that sinθ = cos(θ).

Step-by-step explanation:

To prove that sinθ = cos(90°), we can use the fact that the cosine function is equal to the sine function shifted by 90 degrees. In other words, cos(θ) = sin(θ+90°). Therefore, we can rewrite the equation as sinθ = sin(θ+90°).

Applying the trigonometric identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we can further simplify the equation to sin(θ) = sin(θ)cos(90°) + cos(θ)sin(90°).

Since cos(90°) = 0 and sin(90°) = 1, the equation becomes sin(θ) = sin(θ)(0) + cos(θ)(1), which simplifies to sin(θ) = cos(θ). Hence, we have proved that sinθ = cos(90°).