What is the value of 1 tan 90 deg theta sec 90 deg theta tan 90 deg theta sec 90 deg theta 1 ........

Quantitative Aptitude ( CCS) Trignometry

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What is the value of [1 - tan(90° - θ) + sec(90° - θ)]/[tan(90° - θ) + sec(90° - θ) + 1]?

cot(θ/2)

tan(θ/2)

sin θ

cos θ

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Explanation:

⇒ [1 - tan(90° - θ) + sec(90° - θ)]/[tan(90° - θ) + sec(90° - θ) + 1]
Let the value θ = 30°
⇒ [1 - tan60° + sec60°]/[tan60° + sec60° + 1]
⇒ (1 - √3 + 2)/(1 + √3 + 2)
⇒ {√3(√3 - 1)}/{√3(√3 + 1)}
Rationalizing,
⇒ (√3 - 1)/(√3 + 1) × (√3 - 1)/(√3 - 1)
⇒ (√3 - 1)^2/{(√3)^2 - 12}
⇒ 2 - √3
⇒ tan15° = tan(30°/2) = tan(θ/2)