Question

if x=a secα+b tanα and y=a tanα+b secα, prove that x^2-y^2=a^2 -b^2​

Answer 1

Answer:

Step-by-step explanation:

X^2-y^2

=(a sec@+b tan@)^2 - (a tan@+b sec@)^2

=a^2sec^2@+b^2tan^2@+2absec@tan@-(a^2tan^2@+b^2sec^2@+2absec@tan@

=a^2sec^2@+b^2tan^2@+2absec@tan@-a^2tan^2@-b^2sec^2@-2absec@tan@

=(a^2sec^2@-a^2tan^2@)+(b^2tan^2@-b^2sec^2@)

=(a^2sec^2@-a^2tan^2@)-(b^2sec^2@-b^2tan^2@)

=a^2(sec^2@-tan^2@)-b^2(sec^2@-tan^2@)

=a^2(1)-b^2(1)

=a^2-b^2