Question

x = sec theta + tan theta then
x +1/x =
a)1
b)2
c)2sec theta
d)2tan theta​

Answer 1

Answer:

Option (C) is correct

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

Step-by-step explanation:

$Given \: x=sec\theta+tan\theta \:--(1)$

/* we know the Trigonometric identity:

sec²A - tan²A = 1 */

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

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

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

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

$Now,x+\frac{1}{x}\\=sec\theta+tan\theta+sec\theta-tan\theta$

$=2sec\theta$

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