Question

If tan A = 4/3 then (sin A + cos A) = ?​

Answer 1

Step-by-step explanation:

tanA= perpendicular/ base = 4/3

so we can find the hypotenuse by using Pythagoras theorem

hyp²= base²+ perp²

= 4²+3²

hyp²= 16+9

hyp=√25= 5

we know that sinA= Perp/hyp = 4/5

and cosA = base / hyp= 3/5

so sinA+ cosA= 4/5+3/5= 7/5

Answer 2

Step-by-step explanation:

Given

$tan \: a \: = \frac{4}{3} \\ \\ (sin \: a \: + cos \: a) =$

$\red{We \: know \: that}$ ,

$tan \: a = \frac{(opposite)}{(adjacent)} \\ \\ where \\ \\ opposite \: \: side \: = 4 \\ adjacent \: \: side \: = 3$

$\red{By~Pythagoras~Theorem}$ :-

$=> {(opposite)}^{2} + {(adjaent)}^{2} = {(hypotenuse)}^{2} \\ \\ {(4)}^{2} + {(3)}^{2} = {(hypotenuse)}^{2} \\ \\ 16 + 9 = {(hypotenus)}^{2} \\ \\ 25 = {(hypotenuse)}^{2} \\ \\ hypotenuse = \sqrt{25} \\ \\ hypotenus \: = 5$

:.

$</em></strong><strong><em>\</em></strong><strong><em>b</em></strong><strong><em>l</em></strong><strong><em>u</em></strong><strong><em>e</em></strong><strong><em>{</em></strong><strong><em>S</em></strong><strong><em>in \: </em></strong><strong><em>A</em></strong><strong><em> </em></strong><strong><em>}</em></strong><strong><em> = \frac{(opposite \: side)}{(hypotenuse)} \\ </em></strong><strong><em>→</em></strong><strong><em> </em></strong><strong><em>\</em></strong><strong><em>b</em></strong><strong><em>l</em></strong><strong><em>u</em></strong><strong><em>e</em></strong><strong><em>{</em></strong><strong><em>Si</em></strong><strong><em>n \: </em></strong><strong><em>A</em></strong><strong><em> </em></strong><strong><em>}</em></strong><strong><em> = \frac{4}{5} </em></strong><strong><em>\</em></strong><strong><em>\</em></strong><strong><em> </em></strong><strong><em>\\ and \\</em></strong><strong><em> </em></strong><strong><em>\</em></strong><strong><em>\</em></strong><strong><em> </em></strong><strong><em>\</em></strong><strong><em>p</em></strong><strong><em>i</em></strong><strong><em>n</em></strong><strong><em>k</em></strong><strong><em>{</em></strong><strong><em>C</em></strong><strong><em>os \: </em></strong><strong><em>A</em></strong><strong><em> </em></strong><strong><em>}</em></strong><strong><em>= \frac{(adjacent)}{(hypotenuse)} \\ </em></strong><strong><em>→</em></strong><strong><em> </em></strong><strong><em>\</em></strong><strong><em>p</em></strong><strong><em>i</em></strong><strong><em>n</em></strong><strong><em>k</em></strong><strong><em>{</em></strong><strong><em>Cos</em></strong><strong><em> \: </em></strong><strong><em>A</em></strong><strong><em>}</em></strong><strong><em> = \frac{3}{5}$

:. ( Sin A + Cos A ) =

$=> \frac{4}{5} = \frac{3}{5} \\ \\ => \frac{(4 + 3)}{5} \\ \\ \green{===>} \frac{7}{5}$