Question

if 4 tan A= 3 then find Sin A and Cos A​

Answer 1

To find:-

• Value of sin A and cos A.

Solution:-

Given that,

If 4 tan A = 3

Then tan A = 3/4

$\boxed{ \star \sf \: tan \: \theta = \cfrac{Perpendicular}{Base} }$

$\longrightarrow \sf \: tan \: A = \cfrac{3}{4}$

$\boxed{ \star \sf \: sin \: \theta = \cfrac{Perpendicular}{Hypothenuse} }$

• We don't have Hypothenuse.So,

According to Pythagoras theorem:

$\star \sf {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2}$

Perpendicular = 3

Base = 4

Put the values

$\implies \sf {Hypotenuse}^{2} = {(3)}^{2} + {(4)}^{2}$

$\implies \sf {Hypotenuse}^{2} = 9 + 16$

$\implies \sf {Hypotenuse}^{2} = 25$

$\implies \sf Hypotenuse = \sqrt{25}$

$\implies \sf \bold{ Hypotenuse = 5}$

So,

$\large\boxed{ \sf sin \:A = \dfrac{3}{5} }$

And ,

$\boxed{ \star \sf \: cos \: \theta = \frac{Base}{Hypotenuse} }$

$\large \boxed{ \sf cos \:A = \frac{4}{5} }$

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More ratio's:

$\star \sf \: cosec \: \theta = \dfrac{Hypotenuse}{Perpendicular}$

$\star \sf \: sec \: \theta = \dfrac{Hypotenuse}{Base}$

$\star \sf \: cot \: \theta = \cfrac{Base}{Perpendicular}$