Question

If ( sec X- 1)(sec X+1) =1/3 then cos X=___.


No spam for today pls​

Answer 1

Answer:-

Given,

$\sf( \sec(x) - 1)( \sec(x) + 1) = \frac{1}{3}$

$\sf \implies \sec^{2} (x) - 1 = \frac{1}{3}$

$\sf \implies \sec^{2} (x) =1 + \frac{1}{3}$

$\sf \implies \sec^{2} (x) = \frac{4}{3}$

$\sf \implies \sec (x) = \sqrt{ \frac{4}{3} }$

$\sf \implies \sec (x) = \frac{2}{ \sqrt{3 }}$

$\sf \implies \cos (x) = \frac{ \sqrt{3} }{2}$

Hence,

$\boxed{ \sf \large\cos (x) = \frac{ \sqrt{3} }{2}}$

Answer 2

Step-by-step explanation:

Given,

\sf( \sec(x) - 1)( \sec(x) + 1) = \frac{1}{3}(sec(x)−1)(sec(x)+1)=

3

1

\sf \implies \sec^{2} (x) - 1 = \frac{1}{3}⟹sec

2

(x)−1=

3

1

\sf \implies \sec^{2} (x) =1 + \frac{1}{3}⟹sec

2

(x)=1+

3

1

\sf \implies \sec^{2} (x) = \frac{4}{3}⟹sec

2

(x)=

3

4

\sf \implies \sec (x) = \sqrt{ \frac{4}{3} }⟹sec(x)=

3

4

\sf \implies \sec (x) = \frac{2}{ \sqrt{3 }}⟹sec(x)=

3

2

\sf \implies \cos (x) = \frac{ \sqrt{3} }{2}⟹cos(x)=

2

3

Hence,

\boxed{ \sf \large\cos (x) = \frac{ \sqrt{3} }{2}}

cos(x)=

2

3