Home
Class 11
MATHS
Prove that: sin(60^0-theta)-cos(30^0+the...

Prove that: `sin(60^0-theta)-cos(30^0+theta)=0.`

Text Solution

Verified by Experts

We know that`,sin(60^o +theta)−cos(30^o−theta)`
=`cos[90^o−(60^o +theta)]−cos(30^o−theta)`
=`cos(30^o−theta)−cos(30^o−theta)`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos
  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|193 Videos

Similar Questions

Explore conceptually related problems

Prove that (i) sin(40^(@)-theta)cos(50^(@)+theta)=0 (ii) 1sec(65^(@)+theta)-"cesec"(25^(@)-theta)=0

Prove that :(sin theta cos(90^(0)-theta)cos theta)/(sin(90^(0)-theta))+(cos theta sin(90^(0)-theta)sin theta)/(cos(90^(@)-theta))=1csc^(2)(90^(@)-theta)-tan^(2)theta=cos^(2)(90^(@)-theta)+cos^(2)theta

Evaluate sin(30^(@)+theta)-cos(60^(@)-theta) .

Prove that: 3(sin theta-cos theta)^(4)+6(sin theta+cos theta)^(2)+4(sin^(6)theta+cos^(6)theta)-13=0

Prove that (cos(90^(0)+theta)sec(-theta)tan(180^(@)-theta))/(sec(360^(@)-theta)sin(180^(@)+theta)cot(90^(@)-theta))=-1

Find the value of sin(60+ theta )-cos(30-theta)

Prove that ("cos"(90^0+theta)"sec"(-theta)"tan"(180^0-theta))/("sec"(360^0-theta)"sin"(180^0+theta)"cot"(90^0-theta))=-1.

Prove that f(theta)=(4sin theta)/(2+cos theta)-theta is an increasing function of theta in [0,(pi)/(2)]

Prove that y=(4sin theta)/((2+cos theta))-theta is an increasing function of theta in [0,(pi)/(2)]

Prove that y=(4sin theta)/(2+cos theta)-theta is an increasing function of theta in[0,(pi)/(2)]

RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. Prove that: (cos8^@-"sin"8^@)/(cos8^@+"sin"8^@)=t a n 37^@

    Text Solution

    |

  2. (cos9^@+sin9^@)/(cos9^@-sin9^@)= (a) tan 54^@ (b) tan 36^@ (d) None of...

    Text Solution

    |

  3. Prove that: sin(60^0-theta)-cos(30^0+theta)=0.

    Text Solution

    |

  4. Prove that: sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)=(sqrt...

    Text Solution

    |

  5. Prove that: sin((3"pi")/8-5)cos("pi"/8+5)+cos((3"pi")/8-5)sin("pi"/8+7...

    Text Solution

    |

  6. Prove that :(tan69^@+tan 66^@)/(1-tan 69^@tan66^@)=-1

    Text Solution

    |

  7. If tanA=5/6 and tanB=1/(11),\ p rov e\ t h a t\ A+B=pi/4

    Text Solution

    |

  8. If tanA=m/(m-1)\ and tanB=1/(2m-1), then prove that A-B=\ pi/4

    Text Solution

    |

  9. Prove that: cos^2 45^@-sin^2 15^@=(sqrt(3))/4

    Text Solution

    |

  10. Prove that: sin^2(n+1)A-sin^2n A="sin"(2n+1)A s in A

    Text Solution

    |

  11. Prove that: (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=t a n A

    Text Solution

    |

  12. Prove that: (sin(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+(sin(C-A)...

    Text Solution

    |

  13. Prove that: ("sin"(A-B))/(s in A s in B)+("sin"(B-C))/(s in B s in C)+...

    Text Solution

    |

  14. Prove that: sin^2B=sin^2A+sin^2(A-B)-2sin A cos B sin(A-B)

    Text Solution

    |

  15. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

    Text Solution

    |

  16. Prove that: (tan(A+B))/(cot(A-B))=\ (tan^2A-tan^2B)/(1-tan^2Atan^2B)

    Text Solution

    |

  17. If tan A= xtanB then prove that sin(A-B)/sin(A+B)=(x-1)/(x+1)

    Text Solution

    |

  18. If tan(A+B)=x and tan(A-B)=y then find the values of tan2A and tan2B

    Text Solution

    |

  19. If cos A+sin B=m and sin A+cos B=n , prove that 2sin(A+B)=m^2+n^2-2.

    Text Solution

    |

  20. If tan A+tan B=a and cot A+cot B=b , prove that: cot(A+B)=1/a-1/b

    Text Solution

    |