Question

Find the acute angles A and B satisfying

1)cot(A+B)= 1 , cosec(A-B)= 2

2)secAcotB -secA-2cotB+2=0

Answer 1

Due to byjus rule we are allowed to do 1 question at a time. Be satisfy pls.👍

​​​​​​1) cot (A+B) = 1 , Cosec (A-B) = 2

◎ cot(A+B) = 1/tan(A+B) = 1
.˙. tan(A+B) = 1,
if tanx =1, then x = 45°

(here, i take angle in degrees. You can take in degrees or radians, both are right.)

.˙. A+B= 45°————(1)

◎ cosec (A-B) = 1/Sin(A-B) = 2
.˙. Sin(A-B) = 1/2
if sinx =1/2 , then x= 30°

.˙. A-B = 30°————(2)

Add equ. (1) and (2).
2A = 75
A=37.5°

put value in equ.(1)
B= 45-37.5= 7.5°
B=7.5°