Home
Class 12
MATHS
Let P(n)(u) be a polynomial is u of degr...

Let `P_(n)(u)` be a polynomial is u of degree n. Then, for every positive integern, `sin 2n x` is expressible is

A

`P_(2n)( sin x)`

B

`P_(2n)(cos x)`

C

`cos x P_(2n)-1(sin x)`

D

`sin x P_(2n-1)(cos x)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|13 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|53 Videos
  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

Prove that n^(2)-n divisible by 2 for every positive integer n.

Let P(x) be a polynomial such that p(x)-p'(x)= x^(n) , where n is a positive integer. Then P(0) equals-

Let P(x) be a polynomial of degree n with real coefficients and is non negative for all real x then P(x) + P^(1)(x)+ ...+P^(n)(x) is

Let P(x) be a non-zero polynomial with integer coefficients.If P(n) is divisible for each positive integer n, what is the vale of P(0)?

The expression 31^(n) + 17^(n) is divisible by, for every odd positive integer n :

If a is defined by f (x)=a_(0)x^(n)+a_(1)x^(n-2)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n) where n is a non negative integer and a_(0),a_(1),a_(2),…….,a_(n) are real numbers and a_(0) ne 0, then f is called a polynomial function of degree n. For polynomials we can define the following theorem (i) Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be a real number. if p(x) is divided by (x-a), then the remainder is equal to p(a). (ii) Factor theorem : Let p(x) be a polynomial of degree greater than or equal to 1 and 'a' be a real number such that p(a) = 0, then (x-a) is a factor of p(x). Conversely, if (x-a) is a factor of p(x). then p(a)=0. The factor of the polynomial x^(3)+3x^(2)+4x+12 is

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression (x^(m)y^(n))/((1+x^(2m))(1+y^(2n))) is

Let m be a non-zero integer and n be a positive integer. Let R be the remainder obtained on dividing the polynomial x^(n)+m^(n) by (x-m) . Then

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (More Than One Correct Option Type Questions)
  1. Let f(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)...

    Text Solution

    |

  2. Let P=sin 25^(@) sin 35^(@)sin 60^(@) sin 85^(@) and Q=sin20^(@)sin40...

    Text Solution

    |

  3. let 0ltphiltpi/2, x=sum(n=0)^oocos^(2n)phi, y=sum(n=0)^oosin^(2n)phi a...

    Text Solution

    |

  4. Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos ...

    Text Solution

    |

  5. It is known that sinbeta=4/5 and 0 < beta < pi then the value of (sqrt...

    Text Solution

    |

  6. In cyclic quadrilateral ABCD, if cot A=3/4 and tan B= (-12)/(5), then ...

    Text Solution

    |

  7. If the equation 2cos^(2)x+cosx-a=0 has solutions, then a can be

    Text Solution

    |

  8. If A=sin 44^(@)+cos44^(@), B=sin45^(@)+ cos45^(@) and C= sin46^(@)+cos...

    Text Solution

    |

  9. If tan(2alpha+beta)=x & tan(alpha+2beta)=y, then [ tan3(alpha+beta)]. ...

    Text Solution

    |

  10. If x=secphi-tanphi and y=cosecphi+cotphi then

    Text Solution

    |

  11. If tan(x/2)=cosec x-sin x, thentan^(2)(x/2) is equal to

    Text Solution

    |

  12. If y=(sqrt(1-sin4x)+1)/(sqrt(1+sin 4x)-1), then y can be

    Text Solution

    |

  13. If 3sinbeta=sin(2alpha+beta) then

    Text Solution

    |

  14. Let P(n)(u) be a polynomial is u of degree n. Then, for every positive...

    Text Solution

    |

  15. If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha), then

    Text Solution

    |

  16. If cos 5theta=a cos theta + b cos^(3)theta+c cos^(5) theta+d, then

    Text Solution

    |

  17. x=sqrt(a^2cos^2alpha+b^2sin^2alpha)+sqrt(a^2sin^2alpha+b^2cos^2alpha) ...

    Text Solution

    |

  18. If n is an odd positive interger, then ((cosA+cosB)/(sinA-sinB))^(n)...

    Text Solution

    |

  19. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

    Text Solution

    |

  20. if x = a cos^3 theta sin^2 theta and y = a cos^2 theta sin^3 theta an...

    Text Solution

    |