If sec – tan = m, then the value of sec + tan is Class 10 Maths Introduction to Trigonometry questions with solutions

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Solution

Q.
If sec θ – tan θ = m, then the value of sec θ + tan θ is :

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

2 $m^{2} - 1$

3 $\frac{1}{m}$

4 $- m$

Ans.
(3)

Given, $\sec θ - \tan θ = m$ ...(i)

We know that, $\sec^{2} θ - \tan^{2} θ = 1$

$\Rightarrow (\sec θ - \tan θ) (\sec θ + \tan θ) = 1$

$\Rightarrow m (\sec θ + \tan θ) = 1$

$\Rightarrow \sec θ + \tan θ = \frac{1}{m}$

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