Verify that each equation is an identity.
tan α/sec α = sin α

Guida verificata passo dopo passo

Start by expressing \( \tan \alpha \) and \( \sec \alpha \) in terms of \( \sin \alpha \) and \( \cos \alpha \). Recall that \( \tan \alpha = \frac{\sin \alpha}{\cos \alpha} \) and \( \sec \alpha = \frac{1}{\cos \alpha} \).

Substitute these expressions into the left side of the equation: \( \frac{\tan \alpha}{\sec \alpha} = \frac{\frac{\sin \alpha}{\cos \alpha}}{\frac{1}{\cos \alpha}} \).

Simplify the expression by multiplying the numerator by the reciprocal of the denominator: \( \frac{\sin \alpha}{\cos \alpha} \times \cos \alpha \).

Notice that the \( \cos \alpha \) terms cancel each other out, leaving \( \sin \alpha \).

Conclude that the left side simplifies to \( \sin \alpha \), which matches the right side of the equation, thus verifying the identity.

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