If sec ? – tan ? = m, then the value of sec ? + ta

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Solution

Q.
If $s e c θ - \tan θ = m$ , then the value of $s e c θ + \tan θ$ is

1 $1 - \frac{1}{m}$

2 $m^{2} - 1$

3 $\frac{1}{m}$

4 $- m$

Ans.
(3)

Given $s e c θ - \tan θ = m$

We have to find the value of $s e c θ + \tan θ .$

We know that

${s e c}^{2} θ - {t a n}^{2} θ = 1 \Rightarrow (s e c θ + t a n θ) (s e c θ - t a n θ) = 1 \Rightarrow (s e c θ + t a n θ) m = 1 [Given] \Rightarrow s e c θ + t a n θ = \frac{1}{m}$

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