Home
Class 10
MATHS
If cos theta + sin theta = p and sec the...

If `cos theta + sin theta = p` and `sec theta + cosec theta = q` , prove that `q (p^(2) - 1) = 2p`.

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    KUMAR PRAKASHAN|Exercise Test Your Skills|41 Videos

  • INTRODUCTION TO TRIGONOMETRY

    KUMAR PRAKASHAN|Exercise Practice Thoroughly|19 Videos

  • INTRODUCTION TO TRIGONOMETRY

    KUMAR PRAKASHAN|Exercise Objective Questions|24 Videos

  • COORDINATE GEOMETRY

    KUMAR PRAKASHAN|Exercise Objective Questions (True or false)|5 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    KUMAR PRAKASHAN|Exercise Test Your Skills|48 Videos

Similar Questions

Explore conceptually related problems

If tan theta +sin theta = p and tan theta-sin theta = q , prove that p^(2)-q^(2)=4sqrt(pq)

"cosec" theta =1/2

If x sin^(3)theta + y cos^(3)theta = sintheta costheta and x sin theta = y cos theta , prove that x^(2) + y^(2) = 1.

Show that cot theta +tan theta =sec theta cosec theta

If p and q are the lengths of perpendiculars from the origin to the lines x cos theta - y sin theta = k cos 2 theta and x sec theta + y cosec theta=k respectively, prove that p^(2) + 4q^(2) = k^(2) .

If sec theta=13/12 , find sin theta and cot theta .

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

If f (theta) = |sin theta| + |cos theta|, theta in R , then

If cosec theta + cot theta =k , then prove that cos theta =(k^(2)-1)/( k^(2)+1)

If costheta + sin theta = sqrt2 cos theta , prove that cos theta - sin theta = sqrt2 sin theta .

KUMAR PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Other Important Examples
  1. Evaluate each of the following : 3cos^(2)30^(@)+sec^(2)30^(@)+2cos0^...

    Text Solution

    |

  2. Show that 2(cos^(4)60^(@)+sin^(4)30^(@))-(tan^(2)60^(@)+cot^(2)45^(@...

    Text Solution

    |

  3. Find the value of x in the following equation sin 2x = sin 60° cos 30°...

    Text Solution

    |

  4. If theta is an acute angle and tan theta + cot theta = 2 , find the va...

    Text Solution

    |

  5. Given that sin (A+ B) = sin A cos B + cos A sin B , find the value o...

    Text Solution

    |

  6. Prove that : (cos80^(@))/(sin10^(@))+cos59^(@)cosec31^(@)=2

    Text Solution

    |

  7. Evaluate the following : (2tan53^(@))/(cot37^(@))-(cot80^(@))/(tan10...

    Text Solution

    |

  8. Express sin 72° + cot 72° in terms trigonometric ratios of angles betw...

    Text Solution

    |

  9. Evaluate: ((sin47^(@))/(cos43^(@)))^(2)+((cos43^(@))/(sin47^(@)))^(2)-...

    Text Solution

    |

  10. If sec 5A = cosec (A + 36°) , where 5A is an acute angle, find the va...

    Text Solution

    |

  11. Prove the following : (All angles are acute angles.) sqrt(sec^(2)the...

    Text Solution

    |

  12. Prove the following : (All angles are acute angles.) (1+tan^(2)theta...

    Text Solution

    |

  13. Prove the following : (All angles are acute angles.) (tantheta+sinth...

    Text Solution

    |

  14. Prove the following : (All angles are acute angles.) (sintheta+costh...

    Text Solution

    |

  15. Prove the following : (All angles are acute angles.) tantheta-cotthe...

    Text Solution

    |

  16. If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)thet...

    Text Solution

    |

  17. If cos theta + sin theta = p and sec theta + cosec theta = q , prove t...

    Text Solution

    |

  18. If costheta + sin theta = sqrt2 cos theta, prove that cos theta - sin ...

    Text Solution

    |

  19. Prove that 2 (sin^(6)theta +cos^(6) theta ) - 3(sin^(4)theta +cos^(4...

    Text Solution

    |

  20. If x sin^(3)theta + y cos^(3)theta = sintheta costheta and x sin theta...

    Text Solution

    |