Question

if sin theta = x then find the value of sec theta in terms of x​

Answer 1

SOLUTION

GIVEN

sin θ = x

TO DETERMINE

The value of sec θ in terms of x

EVALUATION

Here it is given that

sin θ = x

Now sec θ

$\displaystyle \sf{ = \frac{1}{ \cos \theta} }$

$\displaystyle \sf{ = \frac{1}{ \sqrt{1 - { \sin}^{2} \theta } } }$

$\displaystyle \sf{ = \frac{1}{ \sqrt{1 - {( \sin \theta)}^{2} } } }$

$\displaystyle \sf{ = \frac{1}{ \sqrt{1 - {( x)}^{2} } } }$

$\displaystyle \sf{ = \frac{1}{ \sqrt{1 - {x}^{2} } } }$

Which is the required expression

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