Question

here are those questions

Answer 1

n)
(tanx+secx-1)/(tanx-secx+1)
multiply the numerator and denominator with (tanx+secx)

(tanx+secx-1)×(tanx +secx)/(tanx-secx+1)×(tanx+secx)

(tanx+secx-1)×(tanx +secx)/(tan²x-sec²x+tanx+secx)

(tanx+secx-1)×(tanx +secx)/(-1+tanx+secx)

(tanx +secx)

sinx/cosx + 1/cosx
(sinx+1)/cosx
hence proved!

8)
(x/a)cosø +(y/b)sinø = 1
square it
(x²/a²)cos²ø +(y²/b²)sin²ø+2(x/a)(y/b)sinøcosø =1

similarly,

(x/a)sinø -(y/b)cosø = 1
square it
(x²/a²)sin²ø +(y²/b²)cos²ø-2(x/a)(y/b)sinøcosø =1

Add both the equations,

(x/a)cosø +(y/b)sinø = 1
square it
(x²/a²){cos²ø + sin²ø}+(y²/b²){sin²ø+cos²ø}=2

(x²/a²)+(y²/b²)=2

Hence proved!