First slide

Trigonometric Identities

Question

If $α, β$ are complementary angles and $\sin α = \frac{3}{5},$ then $\sin α \cos β - \cos α \sin β =$

Moderate

A

$\frac{7}{25}$
B

$- \frac{7}{25}$
C

2
D

3

Solution

$\sin α = \frac{3}{5}, a n d α + β = 90 \Rightarrow β = 90 - α \sin α \cos (90 - α) - \cos α \sin (90 - α) = \sin^{2} α - \cos^{2} α = 2 \sin^{2} α - 1 s u b t u t e$

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