Question

If sec theta = 2, tan theta √3 k , determine the value of k.​

Answer 1

Answer:

given,sec theta=2

sec theta=sec60

theta=60

given, tan theta=root3 k

tan60 root3k

root3 = root3k

k= root3/root3

k=1

Answer 2

The value of k = ± 1

Correct question : If sec θ = 2 , tan θ = √3k determine the value of k.

Given :

sec θ = 2 , tan θ = √3k

To find :

The value of k

Solution :

Step 1 of 2 :

Write down the given equations

Here it is given that , sec θ = 2 , tan θ = √3k

Step 2 of 2 :

Find the value of k

We are aware of the trigonometric identity that ,

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

$\displaystyle \sf{ \implies } {2}^{2} - {( \sqrt{3}k) }^{2} = 1$

$\displaystyle \sf{ \implies }4 - 3 {k}^{2} = 1$

$\displaystyle \sf{ \implies }3 {k}^{2} = 4 - 1$

$\displaystyle \sf{ \implies }3 {k}^{2} = 3$

$\displaystyle \sf{ \implies } {k}^{2} = 1$

$\displaystyle \sf{ \implies }k = \pm \: 1$

Hence the required value of k = ± 1

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