First slide

Trigonometric Identities

Question

If $x = a \sec^{3} θ \tan θ, y = b \tan^{3} θ \sec θ$ , then $\sin^{2} θ$ is equal to

Moderate

A

$\frac{x}{a} - \frac{y}{b}$
B

$\frac{x}{a} + \frac{y}{b}$
C

$\frac{x y}{a b}$
D

$\frac{a y}{b x}$

Solution

$\frac{x}{a} = \frac{\sin θ}{\cos^{4} θ}, \frac{y}{b} = \frac{\sin^{3} θ}{\cos^{4} θ} \Rightarrow \sin^{2} θ = \frac{y}{b} \times \frac{a}{x} = \frac{a y}{b x}$

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