Question

If tan A=44, then Cos A is:​

Answer 1

GIVEN :–

• tan(A) = 44

TO FIND :–

• cos(A) = ?

SOLUTION :–

$\\ \implies { \bold{ \tan(A) = 44 }}$

• We know that –

$\\ \dashrightarrow { \bold{ \tan(A) = \dfrac{ \sin(A) }{ \cos(A) } }}$

• So that –

$\\ \implies { \bold{ \dfrac{ \sin(A) }{ \cos(A) } = 44}}$

• We also know that –

$\\ \dashrightarrow { \bold{ { \sin }^{2} \theta \: + \: { \cos}^{2} \theta = 1 }}$

$\\ \dashrightarrow { \bold{{ \sin}^{2} \theta = 1 - { \cos}^{2} \theta}}$

• So that –

$\\ \implies { \bold{ \dfrac{ \sqrt{1 - { \cos}^{2}(A) }}{ \cos(A) } = 44}}$

• Square on both sides –

$\\ \implies { \bold{ \dfrac{{1 - { \cos}^{2}(A) }}{ \cos^{2} (A) } =1936 }}$

$\\ \implies { \bold{ \dfrac{1}{ \cos^{2} (A) } - \dfrac{{ \cos}^{2}(A) }{{ \cos}^{2}(A)} = 1936}}$

$\\ \implies { \bold{ \dfrac{1}{ \cos^{2} (A) } -1= 44}}$

$\\ \implies { \bold{ \dfrac{1}{ \cos^{2} (A) } = 1936 + 1}}$

$\\ \implies { \bold{ \dfrac{1}{ \cos^{2} (A) } = 1937}}$

$\\ \implies { \bold{\cos^{2} (A) = \dfrac{1}{1937}}}$

• Take square root –

$\\ \longrightarrow \: { \boxed { \bold{\cos (A) = \pm \sqrt{ \dfrac{1}{1937}}}}}$

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Tan A = 44

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of Cos A

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Tan A = 44

As we know

$Tan A = \frac{Sin A }{Cos A}$.......(1)

As, per the Trigonometric identity

${sin}^{2} A + {cos}^{2} A = 1 \\ \\ \implies {sin}^{2} A = 1 - {cos}^{2} A \\ \\ \implies sin A = \sqrt{1 - {cos}^{2} A }$

Therefore:-

Substitute the value of Sin A in equation (1)

$\frac{ \sqrt{1 - {Cos}^{2}A } }{Cos A} = Tan A$

S.O.B.S [ Squaring on both sides]

$\frac{ ({ \sqrt{1 - {cos}^{2} A}) }^{2} }{ {cos}^{2} A} = {44}^{2} \\ \\ \implies \frac{ 1 - {cos}^{2} A}{ {cos}^{2} A} = 1936 \\ \\ \implies \frac{1}{ {cos}^{2} A } - \frac{ {cos}^{2} A}{ {cos}^{2}A } = 1936 \\ \\ \implies \frac{1}{ {cos}^{2} A} - 1 = 1936 \\ \\ \implies \frac{1}{ {cos}^{2}A } = 1936 + 1 \\ \\ \implies \frac{1}{ {cos}^{2} A} = 1937 \\ \\ \implies {cos}^{2} A = \frac{1}{1937}$

$\boxed{Cos A = \pm \sqrt{ \frac{1}{1937} } }$