Home
Class 11
MATHS
If acos theta-b sin theta=c , show that ...

If `acos theta-b sin theta=c ,` show that `asin theta+b cos theta=+-sqrt(a^2+b^2-c^2dot)`

Text Solution

AI Generated Solution

To solve the equation \( A \cos \theta - B \sin \theta = C \) and show that \( A \sin \theta + B \cos \theta = \pm \sqrt{A^2 + B^2 - C^2} \), we can follow these steps: ### Step 1: Start with the given equation We have: \[ A \cos \theta - B \sin \theta = C \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

If a cos theta-b sin theta=c, show that a sin theta+b cos theta=+-sqrt(a^(2)+b^(2)-c^(2))

If a cos theta-b sin theta=c; prove that a sin theta+b cos theta=+-sqrt(a^(2)+b^(2)-c^(2))

Knowledge Check

  • If a cos theta - b sin theta =c , then a sin theta + b cos theta =

    A
    `+- sqrt( (a^(2) + b^(2) - c^(2)))`
    B
    `+- sqrt( (b^(2) + c^(2) - a^(2)))`
    C
    `+- sqrt( (c^(2) + a^(2) - b^(2)))`
    D
    none

  • If a cos theta - b sin theta =c, " then" a sin theta + b cos theta is equal to

    A
    `+- sqrt(a^(2)+b^(2)+c^(2))`
    B
    `+-sqrt(a^(2)+b^(2)-c^(2))`
    C
    `+-sqrt(c^(2)-a^(2)-b^(2))`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    If a cos theta - b sin theta =c , then prove that a sin theta + b cos theta = +- sqrt(a^(2) + b^(2) - c^(2))

    If a cos theta - b sin theta = c, prove that a sin theta + b cos theta = pm sqrt(a^(2) + b^(2) - c^(2)) .

    If a cos theta-b sin theta=c, then a sin theta+b cos theta=+-sqrt(a^(2)+b^(2)+c^(2))(b)+-sqrt(a^(2)+b^(2)-c^(2))(c)+-sqrt(c^(2)-a^(2)-b^(2))(d) None of these

    If a cos theta-b sin theta=c, then find the value of a sin theta+b cos theta

    If a cos theta-b sin theta=c, then find the value of a sin theta+b cos theta

    If a sin theta+b cos theta=c then prove that a cos theta-b sin theta=sqrt(a^(2)+b^(2)-c^(2))

    Home
    Profile