Question

if 5sinA=4, find the value of tanA+secA

Answer 1

$5 \sin(a) = 4 \\ \\ => \sin(a) = \frac{4}{5} \\ \\ \\ \mathbf{we \: know \: \sin(a) = \frac{height}{hypotenuse} }$

Hence,


$\frac{height}{hypotenuse} = \frac{4}{5}$


Now, let height = 4x and hypotenuse = 5x


By Pythagoras theorem,


( 5x )² = ( 4x )² + ( base )²

=> 25x² - 16x² = base²

=> 9x² = base²

=> ( 3x )² = base²

=> 3x





Hence,

tanA + secA

$=> \frac{height}{base} + \frac{base}{hypotenuse} \\ \\ => \frac{4x}{3x} + \frac{3x}{5x} \\ \\ => \frac{4}{3} + \frac{3}{5} \\ \\ => \frac{20 + 9}{15} \\ \\ = > \frac{29}{15}$



tanA + secA = 29 / 15