Question

If sec theta - tan theta = x then show that sec theta + tan theta = 1/x

Answer 1

Given, sec theta-tan theta=x
Now multiply✖ and divide➗ by sec theta + tan theta in sec theta-tan theta in above eqn.
=>1/sec theta + tan theta=x
=>sec theta+tan theta=1/x

Answer 2

HEY Buddy.....!! here is ur answer

Given that :

$\sec\alpha - \tan \alpha = x \\ \\ On \: multiplying \: by \: \sec\alpha + \tan \alpha \: both \: the \: sides :\\ \\ = > ( \sec \alpha + \tan\alpha )( \sec\alpha - \tan \alpha ) = x( \sec \alpha + \tan\alpha ) \\ \\ = > { \sec}^{2} \alpha - { \tan }^{2} \alpha = x( \sec \alpha + \tan\alpha ) \\ \\ As \: we \: know \: that: \: { \sec}^{2} \alpha = 1 + { \tan }^{2} \alpha \\ \\ = > 1 = x( \sec\alpha + \tan \alpha) \\ \\ = > \sec\alpha + \tan\alpha = \frac{1}{x} = R.H.S. \\ \\ HENCE \: PROVED$

I hope it will be helpful for you...!!

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