Question

If x = a sec θ, y = b tan θ, then the value of x²/a² - y²/b², is:
a). 0 b). 1
c). -1 d). None

Note : In case of none, Please Give The Answer Which Is Correct. Thanks²

#APEX GUIDE FOR ALIGARH MUSLIM UNIVERSITY ENTRANCE TEST

Answer 1

HELLO DEAR

x=a×sectheta
=>x²=a²sec²theta

y=b×tantheta
=> y²=b²tan²theta

let theta = alpha

$\frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } \\ \\ = \frac{ {a}^{2} {sec}^{2} \alpha }{ {a}^{2} } - \frac{ {b}^{2} {tan}^{2} \alpha }{ {b}^{2} } \\ \\ = {sec}^{2} \alpha - {tan}^{2} \alpha \\ \\ = \frac{1}{ {cos}^{2} \alpha } - \frac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha } \\ \\ = \frac{1 - {sin}^{2} \alpha }{ {cos}^{2} \alpha } \\ \\ = \frac{ {cos}^{2} \alpha }{ {cos}^{2} \alpha } = 1$
hence option (b) 1 is correct

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hello....

Here is your solution...

Hope this will help you....

Thank you very much......