Question

prove that tan A = sinA/cosA

Answer 1

$<b>HEY THERE!!$

To prove:- tan A = sinA/cosA..........(1)

AS WE KNOW.

TanA= perpendicular/Base(P/B)
SinA = perpendicular / Hypotenuse(P/H)
CosA= Base / Hypotenuse(B/H)

put these values in equation (1)

=>P/B = P/H/B/H
=>P/B = P/B

Hence proved.

Answer 2

We know tanA = $\dfrac{ height \:or\: perpendicular }{ base }$

Divide by hypotenuse on denominator and numerator both on right hand side,

tan A = $\dfrac{\dfrac{perpendicular}{hypotenuse}}{\dfrac{base}{hypotenuse}}$

we know, $\dfrac{perpendicular}{hypotenuse} = sin A$

                 

                $\dfrac{base}{hypotenuse} = cosA$

therefore,

tanA =  $\dfrac{\dfrac{perpendicular}{hypotenuse}}{\dfrac{base}{hypotenuse}}$

tanA = $\dfrac{sinA}{cosA}$

Hence, proved.