Question

If $cos\Theta=\frac{2}{3}$, find the value of $\frac{sec\Theta-1}{sec\Theta+1}$.

Answer 1

SOLUTION :  

Given : cos θ = ⅔  

We have to find the value of : sec θ - 1 / sec θ + 1

sec θ - 1 / sec θ + 1 = (1/cos θ - 1) /( 1/cos θ +1)

=( 1/ ⅔ - 1)/(1/ ⅔ + 1)

= (3/2 - 1) / (3/2 + 1)

= [(3 - 2 )/2] /  [(3 + 2 )/2]

=( ½) / (5/2 )

= ½ × ⅖  

= ⅕

Hence , the value of  sec θ - 1 / sec θ + 1  is 1/5.

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Answer 2

Answer:

$\frac{sec\Theta-1}{sec\Theta+1} = \frac{1}{5}$

Solution:

As we know that

$cos\Theta=\frac{1}{sec \Theta}$

so, if $cos\Theta=\frac{2}{3}$

than

$sec\Theta=\frac{3}{2}$

$\frac{sec\Theta-1}{sec\Theta+1}$

$= \frac{ \frac{3}{2} - 1 }{ \frac{3}{2} + 1} \\ \\ = \frac{ \frac{3 - 2}{2} }{ \frac{3 + 2}{2} } \\ \\ = \frac{1}{5}$