Question

if tan theta=3/4 then find the value of sec theta

Answer 1

Answer:

The value of secθ is ${\frac{5}{4} }$

Step-by-step explanation:

Given: The tan θ = $\frac{3}{4}$

To find: The value of secθ

Solution:

Given: tan θ = $\frac{3}{4}$

We know that

1 + $tan^{2}$ θ = $sec^{2}$θ

we know the value of tan

tan θ = 3/4

⇒ 1 + $( \frac{3}{4})^{2}$ =  $sec^{2}$θ

⇒ 1 + $(\frac{3}{4} )^{2}$ =  $sec^{2}$θ

on squaring 3/4 we get 9/16

⇒ 1 + $\frac{9}{16}$ = $sec^{2}$θ

Take L.C.M and simplify the fraction term

⇒ $\frac{16+9}{16}$ =$sec^{2}$ θ

⇒$\frac{25}{16}$ = $sec^{2}$ θ

⇒secθ = $\sqrt{\frac{25}{16} }$

⇒secθ = ${\frac{5}{4} }$

Final answer:

The value of secθ is ${\frac{5}{4} }$

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Answer 2

The value of sec theta is equal to  $\frac{5}{4}$.

Step-by-step explanation:

According to the given information, we are given that  tan theta = $\frac{3}{4}$.

Now, we know that, the well - known trigonometrical identity that is, adding one to the square of tan theta gives the value as the square of sec theta.

This means that, 1 + tan² theta is equal to sec² theta.

Now, according to the given information, the value of tan theta is given as  $\frac{3}{4}$.

Then, putting this value in the above trigonometrical identity, we get,

1 + tan² theta = sec² theta becomes,

1 + ($\frac{3}{4}$)² = sec² theta

Or, 1 +$\frac{9}{16}$ =  sec² theta

Or, $\frac{16 + 9}{16}$ = sec² theta

Or, sec² theta = $\frac{25}{16}$

Or, sec theta = $\sqrt{\frac{25}{16} }$

Or, sec theta = $\frac{5}{4}$

thus, the value of sec theta is equal to  $\frac{5}{4}$.

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