Home
Class 11
MATHS
Prove that: (i) cos A cos(60^(@)-A)c...

Prove that:
(i) `cos A cos(60^(@)-A)cos (60^(@)+A)=(1)/(4)cos 3A`
(ii) `"tan" A+"tan"(60^(@)+A)-"tan"(60^(@)-A)=3 tan 3A`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY

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

    MODERN PUBLICATION|Exercise Exercise 3(h)Long Answer type Question-I|1 Videos
  • TRIGONOMETRY

    MODERN PUBLICATION|Exercise Exercise 3(g)Short Answer type Question|4 Videos
  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise Chapter test|12 Videos

Similar Questions

Explore conceptually related problems

Prove that: cos A cos(60^(@)-A)cos(60^(@)+A)=(1)/(4)cos3A

Prove that :cos A cos(60-A)cos(60+A)=(1)/(4)cos3A

Prove that: tan A+tan(60^(@)+A)-tan(60^(@)-A)=3tan3A

Prove that: cosA. Cos(60^(@)+A)cos(60^(2)-A)=1/4 cos3A

(ii) Prove cos x cos(60-x)cos(60+x)=(1)/(4)cos3x

Prove that: tan A+tan(60^(@)+A)+tan(120^(@)+A)=3tan3A

Prove that: tanA + tan(60^(@)+A) + tan(120^(@)+A)=3tan3A

tan x * tan (60 ^ (@) + x) * tan (60 ^ (@)-x) = tan3x

Prove that (2cos2A+1)/(2cos2A-1)=tan(60^(@)+A)tan(60^(@)-A)

tan A+tan(60+A)-tan(60-A)=3tan3A

MODERN PUBLICATION-TRIGONOMETRY-Exercise 3(g)Long Answer type Question-I
  1. Prove that: "sin" 4A=4 sin A cos^(3)A-4 cos A "sin"^(3)A.

    Text Solution

    |

  2. If cos theta=(1)/(2)(alpha+(1)/(alpha)),prove that: (i) 2 cos 2thet...

    Text Solution

    |

  3. If x+(1)/(x)=2costheta, then find the valueof x^(3)+(1)/(x^(3)).

    Text Solution

    |

  4. Prove that: (i) cos A cos(60^(@)-A)cos (60^(@)+A)=(1)/(4)cos 3A ...

    Text Solution

    |

  5. cos^2alpha+cos^2(alpha+120^0)+cos^2(alpha-120^0)=3/2

    Text Solution

    |

  6. If tan^2theta=1+2tan^2phi then show that cos2theta+sin^2phi=0

    Text Solution

    |

  7. Find sin x/2 ,cos x/2 and t a n x/2 of the following : s in" "x" "=1/...

    Text Solution

    |

  8. (i) If "tan""(x)/(2)=(m)/(n),prove that m sin x+n cos x=n. (ii) If...

    Text Solution

    |

  9. Prove that (cos^(3)theta-cos 3theta)/(cos theta)+("sin"^(3)theta+"sin"...

    Text Solution

    |

  10. Evaluate: (i) "sin""(3pi)/(8) (ii) "sin""(5pi)/(24) (iii) "tan""(pi...

    Text Solution

    |

  11. Prove that: s in^4pi/8+s in^4(3pi)/8+s in^4(5pi)/8+s in^4(7pi)/8=3/2

    Text Solution

    |

  12. Prove that: (i) "sin"^(2)6x-"sin"^(2)4x="sin" 2x sin 10x (ii) c...

    Text Solution

    |

  13. Find "sin" 7(1^(@))/(2),cos 7(1^(@))/(2) and "tan" 11(1^(@))/(4).

    Text Solution

    |

  14. Prove that: "tan" 142(1^(@))/(2)=2+sqrt2-sqrt3-sqrt6.

    Text Solution

    |

  15. Prove that cotxcot2x-cot2xcot3x-cot3xcotx=1

    Text Solution

    |

  16. Prove that: (i) sin 3x+"sin" 2x-"sin" x =4 sin x cos((x)/(2))cos...

    Text Solution

    |

  17. Prove that cos^2x+cos^2(x+pi/3)+cos^2(x-pi/3)=3/2

    Text Solution

    |

  18. If cos theta=(cos phi-e)/(1-e cos phi),show that: "tan"(theta)/(2)...

    Text Solution

    |