Home
Class 11
MATHS
Q. Prove that from the equality sin^4 al...

Q. Prove that from the equality `sin^4 alpha/a+cos^4 alpha/b=1/(a+b)` follows the relation; `sin^8 alpha/a^3+cos^8 alpha/b^3=1/(a+b)^3.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    ALLEN|Exercise All Questions|114 Videos

Similar Questions

Explore conceptually related problems

Show that : sin^6 alpha+ cos^6 alpha ge 1/4

If 10sin^4 alpha+15 cos^4 alpha=6, then find the value of 27 cosec^6 alpha+8sec^6 alpha.

If alpha satisfies 15 sin^(4)alpha + 10 cos^(4)alpha=6 , then find the value of 27 sin^(8)alpha + 8 cos^(8) alpha

If 10sin^4 alpha +15cos^4alpha=6 then the value of 9cosec^4 alpha + 8 sec^4 alpha-75 is

Prove that cos 4theta–cos 4alpha = 8(cos theta-cos alpha)(cos theta+ cos alpha )(cos theta -sin alpha)(cos theta+sin alpha)

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

If 15 sin^(4)alpha+10cos^(4)alpha=6 , then the value of 8 cosec^(6)alpha+27 sec^(6)alpha is

(cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3 alpha )/( sin alpha ) = 3.

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

Prove that sin ( alpha + 30^(@)) = cos alpha + sin (alpha - 30^(@))

ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove t...

    Text Solution

    |

  2. If tan(pi/4+y/2)=tan^3(pi/4+x/2)dot Prove that (siny)= (sinx)(3+sin^2...

    Text Solution

    |

  3. Q. Prove that from the equality sin^4 alpha/a+cos^4 alpha/b=1/(a+b) fo...

    Text Solution

    |

  4. If P=cos(pi/19)+cos((3pi)/19)+cos((5pi)/19)+....+cos((17pi)/19) and Q=...

    Text Solution

    |

  5. Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)

    Text Solution

    |

  6. If A +B+C=pi, prove that tan^(2)""(A)/(2)+tan^(2)""(B)/(2)+tan^(2)""(C...

    Text Solution

    |

  7. If alpha+beta+gamma=pi, prove that : cos^2 alpha + cos^2 beta + cos^2 ...

    Text Solution

    |

  8. In a DeltaABC, if cot A+cot B+cot C=sqrt3. Prove that the triangle is ...

    Text Solution

    |

  9. If the product (sin1^0)(sin3^0)(sin5^0)(sin7^0)....(sin 89^0)=1/(2^n) ...

    Text Solution

    |

  10. For 0ltthetalt pi/2 the solutions(s) of sum(m=1)^6 cosec (theta+ ((m-1...

    Text Solution

    |

  11. If (1+sint)(1+cot t)=(5)/(4) then find the value of (1-sint)(1-cos t).

    Text Solution

    |

  12. tan^(2)'(pi)/(16)+tan^(2)'(2pi)/(16)+tan^(2)'(3pi)/(16)+tan^(2)'(5pi)/...

    Text Solution

    |

  13. Let x1=prod(r=1)^5cos(rpi)/(11)\ a n d\ x2=sum(r=1)^2cos(rpi)/(11), th...

    Text Solution

    |

  14. The period of the function f(x)=sin^(4)x+cos^(4)x is:

    Text Solution

    |

  15. If y=sec^2theta+cos^2theta,\ theta!=0, then- a.y=0 b. ylt=2 c. ygeq-2 ...

    Text Solution

    |

  16. The value of (1-tan^215^0)/(1+tan^215^0)= (A) 1 (B) sqrt(3) (C) sqrt(3...

    Text Solution

    |

  17. If alpha is a root of 25 cos^2theta+5costheta-12=0, pi/2 < alpha < pi,...

    Text Solution

    |

  18. If sin(alpha+beta)=1, sin(alpha-beta)=1/2 then, tan(alpha+2beta) tan(2...

    Text Solution

    |

  19. If tantheta=-4/3,t h e nsintheta is -4/5b u tnot4/5 (b) -4/5or4/5 ...

    Text Solution

    |

  20. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if (a)x+y!=0 (b)...

    Text Solution

    |