Home
Class 12
MATHS
If sin (x + y) = p/sqrt(1 + p^(2)) " and...

`If sin (x + y) = p/sqrt(1 + p^(2)) " and " cos (x - y) = 1/sqrt(1 + q^(2))`
` "then show that " tan x " is a root of the equation "`
`(p + q)z^(2) + 2(1 - pq) z- (p + q) = 0`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES

    CHHAYA PUBLICATION|Exercise Multiple Correct Answere Type|5 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES

    CHHAYA PUBLICATION|Exercise Integer Answer Type|5 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES

    CHHAYA PUBLICATION|Exercise Short Answer Type Questions|35 Videos

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type )|2 Videos

Similar Questions

Explore conceptually related problems

If , p , q are the roots of the equation x^(2)+px+q=0 , then

If tan ^(-1) ""x + tan ^(-1) ""y + tan ^(-1) ""z=(pi)/(2) and x + y +z = sqrt(3) then show that x =y=z.

If p and q are the roots of the equation x^2+px+q =0, then

Prove that p and q are two roots of the quadratic x^(2)-(p+q)x+pq=0 .

IF 2+sqrt3i is a root of the equation x^2+px+q=0 where p and q are real, find p and q.

If p. q are odd integers. Then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

If p,q are odd integers, then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

if tan ^(-1) x+tan ^(-1)y+tan ^(-1) z=pi/2 and x+y+z= sqrt3 , then show that x=y=z.

The product of the sines of the angles of a triangle is p and the product of their cosines is qdot Show that the tangents of the angles are the roots of the equation q x^3-p x^2+(1+q)x-p=0.

Express the roots of the equation q^2x^2-(p^2-2q)x+1=0 in terms of those of x^2+px+q=0 .

CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES-Long Answer Type Questions
  1. If" " n tan alpha = (n+1) tan beta " then show that", tan (alpha - bet...

    Text Solution

    |

  2. If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (ta...

    Text Solution

    |

  3. If tan theta = sec 2 alpha, "show that", sin 2 theta = (1-tan^(4) alph...

    Text Solution

    |

  4. Prove that,8 cos^(4) theta = 3 + 4 cos 2 theta + cos 4 theta

    Text Solution

    |

  5. Prove that,8 sin^(4) theta = 3 - 4 cos 2 theta + cos 4 theta

    Text Solution

    |

  6. Prove that,64cos^(3) theta sin^(4) theta = cos 7 theta - cos 5 theta -...

    Text Solution

    |

  7. Prove that,sin^(2)A cos^(4) A = 1/16 + 1/32 cos2A - 1/16 cos 4 A - 1/3...

    Text Solution

    |

  8. If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show th...

    Text Solution

    |

  9. If " "alpha " and " beta " are positive acute angles and " cos 2 alpha...

    Text Solution

    |

  10. "If " (tan x)/(tan y) = (1 + cos^(2) x)/(1 + sin^(2) x ) " show that "...

    Text Solution

    |

  11. If sin theta + sin 2 theta = a " and " cos theta + cos 2 theta = b, "...

    Text Solution

    |

  12. If theta = pi/(2^(n) + 1), "show that",2^(n) cos theta cos 2 theta cos...

    Text Solution

    |

  13. Prove that, (2 cos theta - 1)(2 cos 2 theta-1)(2 cos2^(2) theta-1)...(...

    Text Solution

    |

  14. If x-1/x = 2i sin theta, "show that", x^(4)-1/x^(4)=2i sin 4 theta.

    Text Solution

    |

  15. Show that,(x tan alpha + y cot alpha)( x cot alpha + y tan alpha) = (x...

    Text Solution

    |

  16. If u = (1 + cos theta) (1+ cos2 theta) - sin theta sin 2theta, v = s...

    Text Solution

    |

  17. Eliminate theta : x = a ( cos theta + cos 2 theta), y = b ( sin theta ...

    Text Solution

    |

  18. "If " a sin theta + b cos theta = c " and " a cosec theta + b sec thet...

    Text Solution

    |

  19. "If "0ltalphaltpi/2 " and " sin alpha + cos alpha + tan alpha + cot a...

    Text Solution

    |

  20. If sin (x + y) = p/sqrt(1 + p^(2)) " and " cos (x - y) = 1/sqrt(1 + q^...

    Text Solution

    |