If sec θ - cos θ = 14 and 14 sec θ = x, then the value of x is _________.

Question

Question

This question was previously asked in

SSC CHSL 2021 (Held On : 25 May 2022 Shift 2)

Answer 1

Given:

secθ - cosθ = 14 and 14 secθ = x

Concept used:

\(Sec\theta =\frac{1}{Cos\theta}\)

Calculations:

According to the question,

⇒ \(sec\theta - cos\theta= 14\)

⇒ \(\sec\theta-\frac{1}{sec\theta}=14\)

⇒ \( sec²\theta-1=14sec\theta\)

⇒ \(\tan^2\theta=14sec\theta\) ----(\(sec²\theta-1=tan^2\theta\))

\(\ tan²\theta=x\)

∴ The value of x is \(tan²\theta\).

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