Question

If tan α=4/3 then (Sin α + Cos α)=?​

Answer 1

Given -

$\tan( \alpha ) = \frac{4}{3}$

To Find -

$\sin( \alpha ) + \cos( \alpha )$

Solution -

$\tan( \alpha ) = \frac{perpendicular}{base} = \frac{4}{3}$

It means , in a right angled triangle ,

Perpendicular = 4

Base = 3

So, using PGT(Pythagoras Theorem)

Hypotenuse= 5

So,

$\sin( \alpha ) + \cos( \alpha ) = \frac{perpendicular}{hypotenuse} + \frac{base}{hypotenuse}$

so,

$\implies \: \frac{perp \: + \: base}{hypo} \\ \implies \: \frac{4 \: + \: 3}{5} \\ \implies \: \frac{7}{5}$

${\huge{\boxed{\bf{\blue{Answer={\red{\frac{7}{5}}}}}}}}$

Answer 2

Answer:

Given -

\tan( \alpha ) = \frac{4}{3}tan(α)=34

To Find -

\sin( \alpha ) + \cos( \alpha )sin(α)+cos(α)

Solution -

\tan( \alpha ) = \frac{perpendicular}{base} = \frac{4}{3}tan(α)=baseperpendicular=34

It means , in a right angled triangle ,

Perpendicular = 4

Base = 3

So, using PGT(Pythagoras Theorem)

Hypotenuse= 5

So,

\sin( \alpha ) + \cos( \alpha ) = \frac{perpendicular}{hypotenuse} + \frac{base}{hypotenuse}sin(α)+cos(α)=hypotenuseperpendicular+hypotenusebase

so,

\begin{gathered}\implies \: \frac{perp \: + \: base}{hypo} \\ \implies \: \frac{4 \: + \: 3}{5} \\ \implies \: \frac{7}{5}\end{gathered}⟹hypoperp+base⟹54+3⟹57

{\huge{\boxed{\bf{\blue{Answer={\red{\frac{7}{5}}}}}}}}Answer=7/5