Home
Class 11
MATHS
If theta lies in the first quadrant and ...

If `theta` lies in the first quadrant and `costheta=8/(17)` , then prove that `cos(pi/6+theta)+cos(pi/4-theta)+cos((2pi)/3-theta)=((sqrt(3)-1)/2+1/(sqrt(2)))(23)/(17)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|166 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA ENGLISH|Exercise All Questions|196 Videos

Similar Questions

Explore conceptually related problems

If theta lies in the first quardrant and costheta=(8)/( 17 ) , then find the value of cos(30^(@)+theta)+cos(45^(@)-theta)+cos(120^(@)-theta) .

Prove that: 4\ costhetacos\ (pi/3+theta)cos(pi/3-theta)=cos3theta

Prove that : cos^2 theta+ cos^2 ((2pi)/3 -theta) + cos^2 ((2pi)/3 +theta) = 3/2

Prove that: cos^2(pi/4-theta)-sin^2(pi/4-theta)=sin2theta

If theta lies in the first quadrant and 5 tan theta = 4 , " then " (5 sin theta - 3 cos theta )/( sin theta + 2 cos theta )=

Prove that (cos(pi +theta)cos (-theta))/(cos(pi-theta) cos (pi/2+theta))=-cot theta

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

If theta=(pi)/(7), show that cos theta cos 2theta cos 3 theta = (1)/(8) .

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. If t a n(pi//4+theta)+t a n(pi//4-theta)=a , then t a n^2(pi//4+theta...

    Text Solution

    |

  2. If t a n x+tan(x+pi/3)+tan(x+(2pi)/3)=3, then prove that (3tanx-t a n^...

    Text Solution

    |

  3. If theta lies in the first quadrant and costheta=8/(17) , then prove t...

    Text Solution

    |

  4. If tan(A-B)=1,sec(A+B)=2/(sqrt(3)) , then the smallest positive value ...

    Text Solution

    |

  5. If t a nbeta=(nsinalphacosalpha)/(1-nsin^2alpha) , show that tan(alph...

    Text Solution

    |

  6. If A+B=pi/4 , prove that: (1+t a n A)(1+t a n B)=2 (cotA-1)(cot...

    Text Solution

    |

  7. Prove that: cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-c...

    Text Solution

    |

  8. If tan(alpha+theta)=ntan(alpha-theta) , show that (n+1)sin2theta=(n-1...

    Text Solution

    |

  9. Prove that: (sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(co...

    Text Solution

    |

  10. If tan( pi cos theta) = cot ( pi sin theta) then sin (theta + pi/4) e...

    Text Solution

    |

  11. Find the values of the following: sin75^0 (ii) cos75^0 (iii) sin15^0...

    Text Solution

    |

  12. If cotalpha=1/2,secbeta=-5/3,where piltalphalt(3pi)/2and pi/2 ltbetalt...

    Text Solution

    |

  13. If sin A=3/5,0<A<pi/2a n dcosB=(-12)/(13),0<B<(3pi)/2, find the follow...

    Text Solution

    |

  14. Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(ta...

    Text Solution

    |

  15. Prove that: 1/(cos(x-a)cos(x-b))=(tan(x-b)-"tan"(x-a))/(sin(a-b))

    Text Solution

    |

  16. If sin(picostheta)=cos(pi sintheta),t h e n sin2theta=

    Text Solution

    |

  17. If at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2) , where alpha!=beta...

    Text Solution

    |

  18. Prove that: 1/(sin(x-a)sin(x-b))=(cot(x-a)-"cot"(x-b))/(sin(a-b))

    Text Solution

    |

  19. If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi ...

    Text Solution

    |

  20. If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that si...

    Text Solution

    |