Math  /  Trigonometry

Question1 and difference identities. b) sin(π2x)\sin \left(\frac{\pi}{2}-x\right)

Studdy Solution

STEP 1

1. We are asked to find the identity for the expression sin(π2x)\sin \left(\frac{\pi}{2}-x\right).
2. The expression can be simplified using trigonometric identities, specifically the co-function identity for sine and cosine.

STEP 2

1. Identify the relevant trigonometric identity.
2. Apply the identity to simplify the expression.

STEP 3

Identify the relevant trigonometric identity. The co-function identity states:
sin(π2x)=cos(x) \sin\left(\frac{\pi}{2} - x\right) = \cos(x)
This identity is based on the complementary angle relationship between sine and cosine.

STEP 4

Apply the identity to simplify the expression:
Using the identity, we have:
sin(π2x)=cos(x) \sin\left(\frac{\pi}{2} - x\right) = \cos(x)
Thus, the expression simplifies to:
cos(x) \boxed{\cos(x)}

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