Question

if tan theta = 1/2,then sec theta = ​

Answer 1

Answer:

Secα +tanα = 2

We know that sec²α-tan²α=1

This can be written as (secα-tanα)(secα+tanα)=1

Substitute the value of secα+tanα=2 in the above equation from which we get the value of secα-tanα= 1/2

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Answer 2

$\displaystyle \bf sec \theta = \frac{ \sqrt{5} }{2}$

Given :

$\displaystyle \sf \displaystyle \sf tan \theta = \frac{ 1 }{2}$

To find :

The value of sec θ

Solution :

Step 1 of 2 :

Write down the value of tan θ

Here it is given that

$\displaystyle \sf \displaystyle \sf tan \theta = \frac{ 1 }{2}$

Step 2 of 2 :

Find the value of sec θ

We are aware of the formula on Trigonometry that

$\displaystyle \sf 1 + { tan}^{2} \theta = { sec}^{2} \theta$

Thus we get

$\displaystyle \sf \displaystyle \sf tan \theta = \frac{ 1 }{2}$

$\displaystyle \sf{ \implies }{ tan}^{2} \theta = \frac{ 1 }{4}$

$\displaystyle \sf{ \implies }1 + { tan}^{2} \theta = 1 + \frac{ 1 }{4}$

$\displaystyle \sf{ \implies }{ sec}^{2} \theta = \frac{4 + 1 }{4} \: \: \: \bigg[ \: \because \: 1 + { tan}^{2} \theta = { sec}^{2} \theta\bigg]$

$\displaystyle \sf{ \implies }{ sec}^{2} \theta = \frac{5 }{4}$

$\displaystyle \sf{ \implies }{ sec}^{} \theta = \sqrt{ \frac{5 }{4} }$

$\displaystyle \sf{ \implies }{ sec}^{} \theta = \frac{ \sqrt{5} }{2}$

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