Question

if xsinα=ycosα then prove that x/sec2α+y/cosec2α​

Answer 1

Step-by-step explanation:

xsinA=ycosA

sinA/cosA=y/x

tanA=y/x

1/csc2A

=sin2A

=(2tanA/(1-tan²A))

=2xy/x²-y²

y/csc2A=y(2xy)/(x²-y²)

y/csc2A=2xy²/(x²-y²)

1/sec2A

=cos2A

=(1+tan²A)/(1-tan²A)

=x²+y²/x²-y²

1/sec2A=(x²+y²)/(x²-y²)

x/sec2A=x(x²+y²)/(x²-y²)

x/sec2A=x³+xy²/(x²-y²)

x/sec2A+y/csc2A

=x³+xy²/(x²-y²)+2xy²/(x²-y²)

=(x³+xy²+2xy²)/(x²-y²)

=(x³+3xy²)/(x²-y²)