Question

A AND B ARE COMPLIMENTARY angle
Prove that
1+tan A/tan B=sec ²A

Answer 1

Trigonometry,

We have,
A + B = 90°.....(1)

Have to proof that
1 + tanA/tanB =sec²A

Now,
L.H.S.= 1 + tanA/tanB

= 1 + tanA/tan(90°- A) [ from equation 1]

= 1 + tanA/cotA [ tan(90°- e) = cote]

= 1 + tan²A

= sec²A [ as 1 + tan²e = sec²e ]

= R.H.S.

That's it
Hope it helped (^_^メ)