Question

x=3cosecthita+4cotthita,y=4cosecthita-3cotthita , find in terms of x and y

Answer 1

x = 3cosec∅ +4 cot∅
take square both sides,

x² = 9cosec²∅ + 16cot²∅ + 24cosec∅.cot∅ -----(1)

y = 4cosec∅ -3cot∅
take square both sides ,

y² = 16cosec²∅ + 9cot²∅ -24cosec∅.cot∅ ---------(2)

add equations (1) and (2)

x² - y² = 9( cosec²∅ -cot²∅) -16( cosec²∅ - cot²∅)

x² - y² = 9 -16 = -7