Home
Class 12
MATHS
Prove that , a cos theta + b sin the...

Prove that `, a cos theta + b sin theta = sqrt(a^(2) +b^(2) ) cos ( theta - tan ^(-1) ""(b)/(a) )`
`=sqrt(a^(2) +b^(2)) sin (theta +tan ^(-1)""(a)/(b))`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS

    CHHAYA PUBLICATION|Exercise sample questions for competive examination|20 Videos

  • TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS

    CHHAYA PUBLICATION|Exercise Short answer type questions|45 Videos

  • TRANSFORMATIONS OF SUMS AND PRODUCTS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

  • TRIGONOMETRIC RATIOS OF ASSOCIATED ANGLES

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS - ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Prove that, (1 + sin 2 theta - cos 2 theta)/(sin theta + cos theta)= 2 sin theta

If cos theta + sin theta = sqrt2 cos theta , then cos theta - sin theta is___

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

Prove that, cot ( theta + 15^(@))- tan(theta - 15^(@))=(4 cos 2 theta)/(1+2 sin 2 theta)

If sin theta + sin 2 theta = a " and " cos theta + cos 2 theta = b, "show that," (a^(2) + b^(2))(a^(2) +b^(2) -3)=2b

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

Prove that cos theta(sin theta +-sqrt(sin^(2) theta+ sin^(2) alpha)) always lies between +- sqrt(1+sin^(2) alpha) .

If (sin theta + cos theta )=sqrt(2) cos theta , show that cot theta =(sqrt(2)+1).

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

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Long answer type questions
  1. tan ( 2 tan ^(-1)sqrt((1+cos theta)/(1-cos theta)))+ tan theta =0

    Text Solution

    |

  2. tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)...

    Text Solution

    |

  3. cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ...

    Text Solution

    |

  4. (1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan "...

    Text Solution

    |

  5. tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(...

    Text Solution

    |

  6. If cos ^(-1) x+ cos ^(-1) y= theta , show that x^(2)-2xycos thet...

    Text Solution

    |

  7. If sin ( pi cos theta ) = cos (pi sin theta ), , then sho...

    Text Solution

    |

  8. Prove that , a cos theta + b sin theta = sqrt(a^(2) +b^(2) ) cos ...

    Text Solution

    |

  9. IF 2 cos 4 theta + 9 cos 2 theta -7=0 , then show that , theta ...

    Text Solution

    |

  10. cot ^(-1)""x+cot^(-1)""2x=(3pi)/(4)

    Text Solution

    |

  11. cot ^(-1)x+cot^(-1)(a^(2)-x+1)=cot ^(-1)(a-1)

    Text Solution

    |

  12. tan ^(-1)""(1-x)/(1+x)""=(1)/(2) sin ^(-1)""(x)/(sqrt(1+x^(2)))

    Text Solution

    |

  13. sin ^(-1) x+sin ^(-1) (1-x) = cos ^(-1) x

    Text Solution

    |

  14. cos^(-1) ""(5)/(x)+cos^(-1) ""(12)/(x)=(pi)/(2)

    Text Solution

    |

  15. 3 cot ^(-1)""(1)/(2-sqrt(3))+cot ^(-1)""x=(pi)/(2)

    Text Solution

    |

  16. sin^(-1)x+sin ^(-1)""2x=(pi)/(3)

    Text Solution

    |

  17. sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

    Text Solution

    |

  18. sin^(-1)x-sin ^(-1)y=(pi)/(3) and cos^(-1) x+ cos ^(-1) y=(2pi)/(3)

    Text Solution

    |

  19. sin ^(-1)""(ax)/(C ) +sin ^(-1) ""(bx)/(c ) =sin ^(-1)""x where a^(2...

    Text Solution

    |

  20. 2 tan ^(-1) (Cos x) = tan ^(-1) (2 "cosec"x)

    Text Solution

    |