If $sec\theta+tan\theta=7$, then find the value of $sec\theta-tan\theta$.

Given: $ sec\theta +tan\theta =7$.

To do: To find the value of $sec\theta-tan\theta$.

Solution: 

$ sec\theta +tan\theta =7$


$\because sec^{2}\theta -tan^{2}\theta =1$

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

$\Rightarrow  7(sec\theta -tan\theta )=1$

$\Rightarrow  sec\theta -tan\theta =\frac{1}{7}$

Updated on: 10-Oct-2022

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