Question

if sec theta - tan theta = X show that sec theta + tan theta = 1 / X and hence find the value of cos theta

Answer 1

this is required answer

Answer 2

Solution:

We have $sec\theta-tan\theta = x$---(1)

Now ,

By Trigonometric identity:

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

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

$\implies x\cdot(sec\theta+tan\theta)=1$

$\implies sec\theta+tan\theta = \frac{1}{x}$ ----(2)

Now ,

Add equations (1) and (2) , we get

$2sec\theta = x+\frac{1}{x}$

$\frac{2}{cos\theta}= \frac{(x^{2}+1)}{x}$

Do the cross multiplication, we get

$\frac{2x}{(x^{2}+1)}=cos\theta$

Therefore,

$cos\theta =\frac{2x}{(x^{2}+1)}$

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