Home
Class 11
MATHS
The general solution of the equation 7co...

The general solution of the equation `7cos^2theta+3sin^2theta=4` is `theta=2npi+-pi/6,\ n Z` b. `theta=2npi+-(2pi)/3,\ n Z` c. `theta=2npi+-pi/3,\ n Z` d. none of these

Text Solution

AI Generated Solution

To find the general solution of the equation \( 7 \cos^2 \theta + 3 \sin^2 \theta = 4 \), we can follow these steps: ### Step 1: Rewrite the equation We start with the given equation: \[ 7 \cos^2 \theta + 3 \sin^2 \theta = 4 \] We know that \( \sin^2 \theta + \cos^2 \theta = 1 \). Therefore, we can express \( \sin^2 \theta \) in terms of \( \cos^2 \theta \): ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRANSFORMATION FORMULAE

    RD SHARMA|Exercise Solved Examples And Exercises|145 Videos

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos

Similar Questions

Explore conceptually related problems

" The general solution of "7sin^(2)theta+3cos^(2)theta=4" is (where "n in z)

General solution of tan theta+tan4 theta+tan7 theta=tan theta ,whern in Z is theta=(n pi)/(12), whern in Z theta=(n pi)/(9), whern in Ztheta=n pi+(pi)/(12), whern in Z noneofthese

Knowledge Check

  • "cot" theta = "sin" 2 theta, theta ne n pi, n in Z, "if" theta equals

    A
    `45^(@) "or" 90^(@)`
    B
    `45^(@) "or" 60^(@)`
    C
    `90^(@) "only"`
    D
    `45^(@) "only"`

    • Similar Questions

    Explore conceptually related problems

    If A=[cos theta-sin theta sin theta cos theta], then A^(T)+A=I_(2), if theta=n pi,n in Z(b)theta=(2n+1)(pi)/(2),quad n in Z(c)theta=2n pi+(pi)/(3),quad n in Z(d) none of these

    One of the general solutions of sqrt(3)cos theta-3sin theta=4sin2 theta cos3 theta is m pi+(pi)/(18),m in Z(m pi)/(2)+(pi)/(6),AA m in Zm(pi)/(3)+(pi)/(18),m in Z none of these

    y=sin^(2)theta+cos ec^(2)theta,theta!=n pi n in z then

    The value(s) of theta, which satisfy the equation : 2cos^3 3thetatheta+4=3sin^2 3theta is/are (2npi)/3+(2pi)/9,\ n in I (b) (2npi)/3-(2pi)/9,\ n in I\ (2npi)/5+(2pi)/5,\ n in I\ (d) (2npi)/5-(2pi)/5,\ n in I

    The general solution of the equation tan2theta* tantheta = 1 for n in I, theta is equal to (i) (2n+1)pi/4 (ii)npi+-pi/6 (iii)(2n+1)pi/2 (iv) (2n+1)pi/3

    Prove that: cos^(2)theta=cos^(2)alpha then theta=n pi+-alpha,n in Z

    Prove that the general solution of cos theta=cos alpha is given by :theta=2n pi+-alpha where n in Z.

    Home
    Profile