Question

Given that cosec A= -2, sec B= -2, A and B lie in the same quadrant. Find sin (2A+2B)

help me please,​

Answer 1

sin (2A+2B) = 0

Explanation:

Given that,

cosec A= -2 and sec B= -2, A and B lie in the same quadrant.

We need to find the value of sin (2A+2B).

`A=cosec^(-1)(-2)\\\\=-30`

And

`B=\sec^(-1)(-2)\\\\=120^(\circ)`

To find the value of sin (2A+2B) as follows :

sin [2(-30)+2(120)] = sin (-60+240)

=sin (180)

= 0

So, the value of sin (2A+2B) is qual to 0.