Home
Class 10
MATHS
If sintheta+costheta=pandsectheta+"cosec...

If `sintheta+costheta=pandsectheta+"cosec"theta=q` then prove that `q(p^(2)-1)=2p`.

Text Solution

AI Generated Solution

To prove that \( Q(P^2 - 1) = 2P \) given \( P = \sin \theta + \cos \theta \) and \( Q = \sec \theta + \csc \theta \), we will follow these steps: ### Step-by-Step Solution: 1. **Start with the expression for \( P \)**: \[ P = \sin \theta + \cos \theta \] ...
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8a|20 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8 B|22 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|5 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11 B|10 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|8 Videos

Similar Questions

Explore conceptually related problems

If sintheta+costheta=pa n dsectheta+cos e ctheta=q , show that q(p^2-1)=2pdot

If sin theta+ cos theta = p and sec theta + cosec theta = q ; show that q(p^2-1) = 2p

If sin A + cos A = p and sec A + cosec A = q , then prove that : q(p^(2) - 1) = 2 p

If p and q are the lengths of perpendiculars from the origin to the lines xcostheta-ysintheta=kcos2theta and xsec""theta+y" cosec"""theta=""k , respectively, prove that p^2+4q^2=k^2 .

If p and q are the lengths of perpendicular from the origin to the line xcos(theta)-ysin(theta)=kcos(2theta) and xsec(theta)+ycosec(theta)=k respectively , then prove that p^2+4q^2=k^2

If sintheta+costheta=1 , then the value of sin2theta is

If p\ and\ q be the perpendicular form the origin upon the straight lines x s e ctheta+ycosectheta=a\ and\ xcostheta-y sintheta=acos2theta Prove that : 4p^2+q^2=a^2\ dot

If sintheta + 2 costheta=1 ,then prove that 2sintheta-costheta=2 .

(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

If cosec theta + cot theta = p prove that cos theta = p2-1 / p2 + 1

NAGEEN PRAKASHAN ENGLISH-INTRODUCTION TO TRIGONOMETRY-Problems From NCERT/exemplar
  1. In P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine ...

    Text Solution

    |

  2. Prove that : sqrt((1-cos^(2)theta)sec^(2)theta)=tantheta

    Text Solution

    |

  3. Prove (tantheta+2)(2tantheta+1)=5tantheta+2sec^2theta.

    Text Solution

    |

  4. If cosA+cos^(2)A=1, then prove that sin^(2)A+sin^(4)A=1.

    Text Solution

    |

  5. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

    Text Solution

    |

  6. Show that 1+cot^2alpha / (1+cosec alpha)=cosec alpha

    Text Solution

    |

  7. (sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

  9. If 2sin^(2)theta-cos^(2)theta=2, then find the value of theta.

    Text Solution

    |

  10. if tantheta+sectheta=l then prove that sectheta=(l^2+1)/(2l)

    Text Solution

    |

  11. If asintheta+bcostheta=c then prove that acostheta-bsintheta=sqrt(a^2+...

    Text Solution

    |

  12. If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(...

    Text Solution

    |

  13. Prove that : tantheta+tan(90^(@)-theta)=sectheta*sec(90^(@)-theta)

    Text Solution

    |

  14. Shown that : tan48^(@)tan23^(@)tan42^(@)tan67^(@)=1

    Text Solution

    |

  15. If tan A= cot B. prove that : A+B=90^(@)

    Text Solution

    |

  16. Express sin 67^(@)+cos75^(@) in terms of trigononmertic ratios of angl...

    Text Solution

    |

  17. If tan A=cot (A-18^(@)) where 2A is an acute angle , find the value of...

    Text Solution

    |

  18. If s e c4A=cos e c(A 20o) , where 4A is an acute angle, find the v...

    Text Solution

    |

  19. The value of the expression cosec (75^(@)+theta) - sec(15^@)-theta)-ta...

    Text Solution

    |

  20. If cos(alpha + beta)=0, then sin(alpha-beta) can be reduced to

    Text Solution

    |