If 0<θ,ϕ<π/2 and x=∑n=0∞ sin2n⁡ϕ, y=∑n=0∞ cos2n⁡θ and z=∑n=0∞ cosn⁡(θ+ϕ)cosn⁡(θ−ϕ), then

If 0<θ,ϕ<π/2 and x=n=0sin2nϕ, y=n=0cos2nθ and z=n=0cosn(θ+ϕ)cosn(θϕ), then

  1. A

    xyz+1=yz-zx

  2. B

    xyz-1=yz+zx

  3. C

    xyz-xy=yz-zx

  4. D

    xyz+1=yz+zx

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    We have x=11sin2ϕ=1cos2ϕ,
    y=11cos2θ=1sin2θ,

    Also, cos(θ+ϕ)cos(θϕ)=cos2ϕsin2θ=1x1y
    As, 0<cos2ϕ<1,0<sin2θ<1,1<cos2ϕsin2θ<1
     1<1x1y<1
    Thus, z=n=01x1yn=111x1y=xyxyy+x
     z(xyy+x)=xy or xyzxy=yzxz

    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.