Question

prove the following identity : (sinA+cosecA)²+(cosA+secA)²=5+sec²A-cosec²A​

Answer 1

Answer:

(sinA+cosecA)square

sin square A + cosec squareA+ 2 sin A .cosecA

sin squareA + cosec square A + 2 sinA .1/ sinA

sin squareA+ cosec squareA + 2

(cosA + sec A)square

cos squareA+ sec squareA + 2 cosA . secA

cos squareA+ sec squareA + 2cosA . 1/cosA

cos squreA + sec squareA + 2

1 & 2 equation add

(sin squareA + cosec squareA+2 ) + (cos squareA + sec squareA +2)

( sin square A+ cos squareA = 1)

5 + sec squareA + cosec squareA