Question

If tan0 =3/4 then find the value of
Sec0.​

Answer 1

Question:-

If tan θ =3/4 then find the value of Sec θ .

Answer:-

• The value of sec θ is 5/4.

To find:-

• Value of sec θ

Solution:-

$\large{ \tt : \implies \: \: \: \: \tan \theta = \frac{3}{4} } \\ </p><p></p><h3><strong>We</strong><strong> </strong><strong>have</strong><strong>, </strong></h3><p></p><p></p><ul><li><strong>Sec</strong><strong>²</strong><strong>θ</strong><strong> </strong><strong>=</strong><strong> </strong><strong>1</strong><strong> </strong><strong>+</strong><strong> </strong><strong>tan</strong><strong>²</strong><strong>θ</strong></li></ul><p></p><p><strong>[tex]\large{ \tt : \implies \: \: \: \: { \sec}^{2} \theta = 1 + { \frac{3}{4} }^{2} }$

$\large{ \tt : \implies \: \: \: \: { \sec}^{2} \theta = 1 + \frac{9}{16} }$

$\large{ \tt : \implies \: \: \: \: { \sec}^{2} \theta = \frac{16 + 9}{16} }$

$\large{ \tt : \implies \: \: \: \: { \sec}^{2} \theta = \frac{25}{16} }$

$\large{ \tt : \implies \: \: \: \: \sec \theta = \sqrt{ \frac{25}{16} } }$

$\large{ \tt : \implies \: \: \: \: { \boxed{\sec \theta = \frac{5}{4} }}}$

• The value of sec θ is 5/4.

Answer 2

Given

• tanθ = 3/4

⠀

To find

• The value of secθ.

⠀

Solution

• We know that

⠀

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{sec^2θ = 1 + tan^2θ{\bigstar}}}}$

⠀⠀

★ Putting the values

$\tt\longmapsto{sec^2θ = 1 + (\dfrac{3}{4})^2}$

⠀

$\tt\longmapsto{sec^2θ = 1 + \dfrac{9}{16}}$

⠀

$\tt\longmapsto{sec^2θ = \dfrac{16 + 9}{16}}$

⠀

$\tt\longmapsto{sec^2θ = \dfrac{25}{16}}$

⠀

$\tt\longmapsto{secθ = \sqrt{\dfrac{25}{16}} }$

⠀

$\tt\longmapsto{secθ = ±\dfrac{5}{4}}$

⠀

Hence, the value of secθ is $\tt\longmapsto{\dfrac{5}{4}}$

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