Discuss Forum

1. if secθ+tanθ=x,then tanθ is-

  • A. x2+1/x
  • B. x2+1/x
  • C. x2+1/x
  • D. x2+1/x

Answer: Option D

Explanation:

Step - by - step explanation:

Given : sec θ + tan θ = x …….. (1)

By using an identity , sec² θ - tan² θ = 1

(sec θ + tan θ)(sec θ - tan θ) = 1

[By using identity , a² - b² = (a + b) (a - b) ]

x (sec θ - tan θ) = 1

(sec θ - tan θ) = 1/x ……….(2)

On Subtracting eq 1 & 2,

sec θ + tan θ - (sec θ - tan θ) = (x - 1/x)

sec θ + tan θ - sec θ + tan θ) = (x - 1/x)

2 tan θ = (x - 1/x)

2 tan θ = (x² - 1)/x

tan θ = (x² - 1)/2x

Hence, the value of tan θ is (x² - 1)/2x.

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