Question

Evaluate: tan 41degree
/cos49degree

Answer 1

$\frac{tan41}{cos49} \\ \\ = \frac{tan 41}{sin \: 41} \\ \\ = \frac{ \frac{sin \: 41}{cos41} }{sin41} \: \: \: \: \:\:\:\:\:\: [tanA = \frac{sinA}{cosA}] \\ \\ = \frac{sin41}{cos41sin41} \\ \\ = \frac{1}{cos41} \\ \\ = sec41$

Answer 2

Hi

(tan41°)/(cos49°)

=(tan41°)/(cos90-41)

=(tan41)/(sin41)

=(hieght/base)/(hieght/hypotenuse)

Hieght will cancel

=(hypotenuse/base)

=sec41°

I hope this will help you

-by ABHAY