Question

Help me prove that sec(a-b) =seca*secb/1+tana*tanb​

Answer 1

Use:

`sec a=(1)/(cos a)`

Answer 2

See below.

Explanation:

Write the sec's as 1 / cos and the tan's as sin / cos

I will write sin as s and cos as c:

Left side = 1 / ( cos)a - b) = 1 / (ca cb + sa sb)

Right side = 1 / ( ca cb ( 1 + sa sb / ca cb))

= 1 / ( ca cb * ( ca cb + sa sb) / ca cb)

The 'ca cb' cancels out so

Right side = 1 / (ca cb + sa sb) = left side..