Question

How do you prove `(tan b + cotb) /(cot b - tan b) = sec 2b`?

Answer 1

Prove trig expression

Explanation:

Numerator of left side:
#sin B/(cos B) + cos B/(sin B) = (sin^2B + cos^2 B)/(sin B.cos B) = = 1/(sin B.cos B)# (1)
Denominator of left side:
#cos B/(sin B) - sin B/(cos B) = (cos^2 B - sin^2 B)/(sin B.cos B) = = (cos 2B)/(sin B.cos B) #.(2)

`(N(1))/(D(2)) = (1/(sin B.cos B))((sin B.cos B)/(cos 2B))` =
`= 1/(cos 2B) = sec 2B`