Home
Class 11
MATHS
If x = sum(n = 0)^(infty) cos ^(2n) thet...

If x = `sum_(n = 0)^(infty) cos ^(2n) theta, " "y = sum_(n = 0)^(infty) sin^(2n) theta and `
` z = sum_(n = 0)^(infty) cos^(2n) theta sin^(2n)theta, 0 lt theta lt (pi)/(2)`, then show that
xyz = x + y + z
[ Hint : use the formula `1 + x + x^(2) + x^(3)` +...
`=(1)/(1 - x)`, where |x|`lt`1 ]

Text Solution

Verified by Experts

The correct Answer is:
`therefore` x + y + z = xyz
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    SURA PUBLICATION|Exercise EXERCISE 3.2|19 Videos

  • TRIGONOMETRY

    SURA PUBLICATION|Exercise EXERCISE 3.3|17 Videos

  • SURAS MODEL QUESTION PAPER -2

    SURA PUBLICATION|Exercise section -IV|7 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY

    SURA PUBLICATION|Exercise ADDITIONAL PROBLEMS - SECTION - D|3 Videos

Similar Questions

Explore conceptually related problems

If xsum_(n=0)^(oo)cos^(2n)theta,y=sum_(n=0)^(oo)sin^(2n)thetaandz=sum_(n=0)^(oo)cos^(2n)thetasin^(2n)theta,ltthetalt(pi)/(2), then show that xyz = x + y + z.

If 0 lt phi lt (pi)/(2) , x= sum_(n=0)^(oo) cos^(2n) phi ,y sum _(n=0)^(oo) sin ^(2n) phi and z = sum _(n=0) ^(oo) cos ^(2n) phi sin ^(2n) phi , then

Solve : 5cos2theta+2cos^2(theta/2)+1=0,-pi lt theta lt pi

sin^2 n theta- sin^2 (n-1)theta= sin^2 theta where n is constant and n != 0,1

If (sin 3theta)/(cos 2theta)lt 0 , then theta lies in

If |2 sin theta-cosec theta| ge 1 and theta ne (n pi)/2, n in Z , then

Find the value of sum_(n=1)^(infty) 1/(2n-1) (1/9^(n-1) + 1/9^(2n-1))

If xsin^(3) theta +y cos^(3) theta=sin theta cos theta and x sin theta =y cos theta , then prove that x^(2)+y^(2)=1 .

If theta in (pi//4, pi//2) and sum_(n=1)^(oo)(1)/(tan^(n)theta)=sin theta + cos theta , then the value of tan theta is