Home
Class 12
MATHS
if un=cos^nalpha+sin^nalpha show that, 2...

`if u_n=cos^nalpha+sin^nalpha` show that, `2u_6-3u_4+1=0`

Text Solution

Verified by Experts

The correct Answer is:
`=2-6 cos^2alpha-3+6cos^2alpha sin^2alpha+1=0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise EXERCISE 2|94 Videos

  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|1 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

  • VECTOR

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION|18 Videos

Similar Questions

Explore conceptually related problems

If u_n=sin ^n alpha+cos^nalpha then show that, the value of 6u_4-4u_6 is independent of alpha .

If u_(n)=sin^(n)alpha+cos^(n)alpha , then prove that 2u_(6)-3u_(4)+1=0 .

If u_n=cos^ntheta+sin^ntheta then 2u_6-ku_4+1=0 then the numerical quantity k must be equal to

If u_n=sin^("n")theta+cos^ntheta, then prove that (u_4-u_6)/(u_2-u_4)=1/2 .

If u_n=sin^("n")theta+cos^ntheta, then prove that (u_5-u_7)/(u_3-u_5)=(u_3)/(u_1) .

If u_(n)=2 cos n theta , then show that u_(n+1)= u_(1)u_(n)-u_(n-1) , hence, show that 2 cos 5 theta= u_(1)^(5)- 5u_(1)^(3)+ 5u_(1)

If u_(n)=int_(0)^((pi)/(4))tan^(n)xdx , show that, u_(n)+u_(n-2)=(1)/(n-1)(ngt1) , hence find u_(5)

A train of mass M is in motion. When its velocity is u_1 and acceleration is a_1 , resistive force against its speed is R_1 . Also when velocity is u_2 and acceleration is a_2 , resistive forced is R_2 . If the engine works at a fixed rate P, show that P(u_2-u_1)=u_1u_2(R_1-R_2)+Mu_1u_2(a_1-a_2) .

If t be a variable parameter, find the vartex, axis, focus and length of the latus rectum of the parabola whose parametric equations are, x = u cos alpha* t, y = u sin alpha * t - (1)/(2) "gt"^(2) .