Home
Class 11
MATHS
If "sin"A=(1)/(2)(x+(1)/(x)),prove that:...

If `"sin"A=(1)/(2)(x+(1)/(x))`,prove that:
`"sin" 3A+(1)/(2)(x^(3)+(1)/(x^(3)))=0`.

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise NCERT EXAMPLES|6 Videos
  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise Exercise 3(a) Short Answer type Question|13 Videos
  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise Chapter Test (3)|12 Videos
  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise Chapter test|12 Videos

Similar Questions

Explore conceptually related problems

If cos x + cos y =(1)/(3) and sin x + sin y=(1)/(4) prove that tan ((x+y)/(2))=(3)/(4)

Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^(3)),x in[-(1)/(2),(1)/(2)]

If

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

If tan((pi)/(4)+(y)/(2))=tan^(3)((pi)/(4)+(x)/(2))* Prove that (sin y)/(sin x)=(3+sin^(2)x)/(1+3sin^(2)x)

If sin^(3)x cos3x+cos^(3)x sin3x=(3)/(8), then the value of sin4x is (1)/(2)(b)1(c)-(1)/(2)(d)0

Prove that sin^(-1)(3x-4x^3)=3sin^(-1)x,x in[1/2,1]

If f(x)=sin^(-1)x then prove that lim_(x rarr(1)/(2))f(3x-4x^(3))=pi-3lim_(x rarr(1)/(2))sin^(-1)x

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)), then prove that (dy)/(dx)=(sin^(-1)x)/((1-x^(2))^((3)/(2)))

Solve sin^(-1)x+sin^(-1)2x=(pi)/(3)

MODERN PUBLICATION-TRIGONOMETRY-FREQUENTLY ASKED QUESTIONS
  1. Prove that n( " cos " 4x + " cos " 3x + " cos " 2x)/(" sin " 4x +...

    Text Solution

    |

  2. (( sin 7x + sin 5x)+(sin 9x + sin 3x))/((cos 7x + cos 5x)+(cos 9x+ cos...

    Text Solution

    |

  3. Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha...

    Text Solution

    |

  4. If s intheta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/...

    Text Solution

    |

  5. If alpha+beta+90^0 , find the maximum and minimum values of s inalphas...

    Text Solution

    |

  6. Prove that (tan 5theta + tan 3theta)/(tan 5theta - tan 3theta) = 4 c...

    Text Solution

    |

  7. Find "sin" 2theta when "sin" theta+cos theta=1.

    Text Solution

    |

  8. Prove that: "tan"A+cotA=2"cosec" 2A and deduce that "tan" 75^(@)+co...

    Text Solution

    |

  9. Prove that (i) (sec 8A -1)/(sec 4A -1) =(tan 8A)/(tan 2A) (ii) (c...

    Text Solution

    |

  10. If tan (alpha-beta)=(sin 2beta)(3-cos 2beta), then

    Text Solution

    |

  11. Prove that: cos A cos 2A cos 2^(2)A cos 2^(3)A….....cos 2^(n-1)A=("sin...

    Text Solution

    |

  12. If "sin"A=(1)/(2)(x+(1)/(x)),prove that: "sin" 3A+(1)/(2)(x^(3)+(1)...

    Text Solution

    |

  13. Prove that: cos^(2)pi/8 + cos^(2)(3pi)/(8) + cos^(2)(5pi)/(8)+ cos^(...

    Text Solution

    |

  14. Prove that: cos 6x=32 cos^(6)x-48 cos^(4)x+18 cos^(4)x+18 cos^(2)x...

    Text Solution

    |

  15. sqrt2+ sqrt3+sqrt4+sqrt6 is equal to

    Text Solution

    |

  16. Find the value of "tan" 22^(@) 30'.

    Text Solution

    |

  17. Prove that:tan4x=(4tanx(1-tan^2x))/(1-6tan^2x+tan^4x)

    Text Solution

    |

  18. If "sin" theta+"sin" phi=a and cos theta+cos phi=b find: (i) "sin"(...

    Text Solution

    |

  19. If "tan" x=(3)/(4),piltxlt(3 pi)/(2), find the values of "sin"(x)/(2),...

    Text Solution

    |

  20. If alphaa n dbeta are distict roots of acostheta+bs intheta=c , prove ...

    Text Solution

    |