Question

(sec θ − cos θ)² − (sec θ + cos θ)² is equal to ______.

Options

• 4

• 2

• −2

• −4

Answer 1

(sec θ − cos θ)² − (sec θ + cos θ)² is equal to −4.

Explanation:

Solving,

⇒ (sec θ − cos θ)² − (sec θ + cos θ)²

⇒ (sec θ − cos θ + sec θ + cos θ)[(sec θ − cos θ) − (sec θ + cos θ)] [∵ a² − b² = (a + b)(a - b)]

⇒ (sec θ − cos θ + sec θ + cos θ)(sec θ − sec θ − cos θ − cos θ)

⇒ 2 sec θ.(−2 cos θ)

⇒ −4.sec θ.cos θ

\[\Rightarrow -4 \times \frac{1}{\cos \theta} \times \cos \theta\]

⇒ −4