Question

If Sec A = 5/3, the value of
Tan A is
O 3/4
O 3/5
O 5/4
O 4/3​

Answer 1

⇝ Given :-

• $\rm secA = \frac{5}{3}$

⇝ To Find :-

• $\text{Value of tanA}$

⇝ Solution :-

We Have,

$\rm secA = \frac{5}{3}$

⏩ Squaring Both Side :

$:\longmapsto \rm {sec}^{2} A = \bigg( \frac{5}{3} \bigg)^{2}$

$:\longmapsto \rm {sec}^{2}A = \frac{25}{9}$

We Know that,

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{  {sec}^{2}A = 1 + {tan}^{2}A }}}$

$:\longmapsto \rm1 + tan {}^{2} A = \frac{25}{9}$

$:\longmapsto \rm {tan}^{2} A = \frac{25}{9} - 1$

$:\longmapsto \rm {tan}^{2} A = \frac{25 - 9}{9}$

$:\longmapsto \rm {tan}^{2} A = \frac{16}{9}$

$:\longmapsto \rm tanA = \sqrt{ \frac{16}{9} }$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf tanA= \frac{4}{3} } }}}$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{\text Value \: of \: tan \text A = \frac{4}{3} }}}}}$

Hence,

$\Large\red\maltese\:\:\underline{\green{\underline{\frak{\pmb{4th \: Option \: is \:Correct}}}}}$

Answer 2

Answer:

Question : -

• If
• $sec \: A = \frac{5}{3}$
• The value of tan A is

1. $\frac{3}{4}$
2. $\frac{3}{5}$
3. $\frac{5}{4}$
4. $\frac{4}{3}$

Given :-

• $sec \: A = \frac{5}{3}$

To find :-

• $The \: value \: of \: tan \: A$

Explanation :-

• Here first squaring on both the sides we get that,

• $sec {}^{2} A = ( \frac{5}{3} ) {}^{2}$

• ${sec}^{2} A = \frac{25}{9}$

• Here we should use the formula of trigonometric identities we get that,

${sec}^{2} A = 1 + {tan}^{2} A$

• $1 + {tan}^{2} A = \frac{25}{9}$
• ${tan}^{2} A = \frac{25}{9 } - 1$

• ${tan}^{2} A = \frac{25 - 9}{9}$

• ${tan}^{2} A = \frac{16}{9}$

• $tan \: A = \sqrt{ \frac{16}{9} }$

• $tan \: A = \frac{4}{3}$

Therefore,

• The value tanA=4/3.

Hope it helps u mate .

Thank you .