Question

If x=asin Z and y=btan C to prove asquare upon xsquare-bsquare upon ysquare=1

Answer 1

x=asinC, y=btanC
∴,a²/x²-b²/y²
=a²/a²sin²C-b²/b²tan²C
=1/sin²C-1/tan²C
=(tan²C-sin²C)/sin²Ctan²C
={(sin²C/cos²C)-sin²C}/sin²C(sin²C/cos²C)
=sin²C(1/cos²C-1)/sin²C(sin²C/cos²C)
={(1-cos²C)/cos²C}/{sin²C/cos²C}
=(1-cos²C)/sin²C
=1/sin²C-cos²C/sin²C
=cosec²C-cot²C  [∵, cosec²C-cot²C=1]
=1 (Proved)