Question

if tan theeta =5/12 ,theeta is acute angle.then the value of sec theeta +cosec theeta...?

Answer 1

Hi there :)

Look at the attachment

Thanks !

Answer 2

tan A = $\dfrac{5}{12}$



$\dfrac{height}{base}= \dfrac{5}{12}$



Let the value of height be 5x and base be 12x,


$\:\:\:\:\:\underline{By\: Pythagoras\:Theorem}$


Hypotenuse² = ( height )² + ( base )²


hypotenuse² = ( 5x )² + ( 12x )²


hypotenuse² = 25x² + 144x²


hypotenuse² = 169x²


hypotenuse = 13 x




Therefore,

sec A = $\dfrac{hypotenuse}{base}= \dfrac{13x}{12x}= \dfrac{13}{12}$



cosecA = $\dfrac{hypotenuse}{height}= \dfrac{13x}{5x} = \dfrac{13}{5}$





Hence,



secA + cosecA


$\dfrac{13}{12} +\dfrac{13}{5}$


$\dfrac{221}{60}$


secA + cosecA = 221 / 60