Question

please solve this problem​

Answer 1

Step-by-step explanation:

Pls refer to the attachment for the detailed solution.

Answer 2

one squaring both the sides

(x/ycostheta + y/bsintheta)^2 = (1)^2

x^2/a^2cos^2 theta+y^2/b^2sin^2 theta+ 2x/a*y/b costheta bsintheta=1................equation 1

now

squaring both the sides

(x/asintheta+y/bcostheta)^2=(1)^2

x^2/a^2sin^2theta+y^2/b^2cos^2theta-2x/a*y/b costheta sintheta=1................equation 2

Now by adding both the equation

we get

x^2/a^2cos^theta+x^2/a^2sin^2theta+y^2/b^2 sin^2theta+y^2/b^2cos^2theta=2

x^2/a^2(sin^2theta+cos^2theta)+y^2/b^2(sin^2theta+cos^2theta)=2

x^2/a^2+y^2/b^2=2

hence proved