Question

Complete the identity. =( sin (alpha +beta))/ (cos alpha cos beta)=?

A. cot α + cot β
B. tan β + tan α
C. tan α + tan β
D. -tan α + cot β

Answer 1

Hi, We know:

Sin(a + b) = 2.Sin(a).Sin(b)

Then,

= 2Sin(a).Cos(b)/Cos(a).Cos(b)

Canceling Cos(b)

= 2Sin(a)/Cos(a)

As Tan(a) = Sin(a)/Cos(a)

Then we will stay:

= 2Tan(a)

Or

= Tan(a) + Tan(a)

There is anything wrong on the alternatives