Question

Find the acute angles A and B satisfying
(i) cot (A+B) = 1, cosec (A-B) = 2
(ii) sec A cot B - sec A - 2 cot B + 2 = 0

Answer 1

Question 1st

Solution :-

cot( A + B ) = 1

cot( A + B ) = cot45°

A + B = 45° ________(1)

cosec ( A - B ) = cosec30°

A - B = 30° __________(2)

Adding 1st and second

A + B = 45°
A - B = 30°
__________
2A = 75°

A = 75° /2= 37.5 °

Putting the value of B on 1st 37.5° + B = 45°
B = 7.5°
_______________________
Question:2nd

Solution :-

SecA * cotB - secA - 2cotB + 2 = 0

secA ( cotB - 1) - 2 ( cotB - 1) = 0

(secA - 2) ( cotB - 1) = 0

secA = 2

secA = sec60 °

A = 60°

and , cotB - 1 = 0

cotB = cot45°

B = 45°

_____________________

Hope it helps !! :'(