Home
Class 11
MATHS
Prove that (cos2theta)/(1+sin2theta)=tan...

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

Text Solution

Verified by Experts

LHS`(cos2theta)/(1+sintheta)=(cos^2theta-sin^2theta)/(costheta+sintheta)^2=(costheta-sintheta)/(costheta+sintheta)`
`(1-tantheta)/(1+tantheta)=tan(pi/4-theta)`=R.H.S`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MEASUREMENT OF ANGLES & TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|25 Videos

  • PARABOLA, ELLIPSE AND HYPERBOLA

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

Prove that: (sin2theta)/(1+cos2theta)=tantheta

Prove that sintheta/(cos3theta)+(sin3theta)/(cos9theta)+(sin9theta)/(cos27theta)=1/2(tan27theta-tantheta)

Knowledge Check

  • (1-cos2theta)/(sin2theta)=

    A
    `sintheta`
    B
    `cos theta`
    C
    `tan theta`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

    Prove that: (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

    Prove that 4 sin theta sin(pi/3 + theta) sin (pi/3-theta) = sin 3 theta

    By using properties of determinats. Prove that- |(sintheta,costheta,sin2theta),(sin(theta+(2pi)/3), cos(theta + (2pi)/3) ,sin(2theta + (4pi)/3)),(sin(theta-(2pi)/3) ,cos(theta - (2pi)/3), sin (2theta - (4pi)/3))|= 0

    If cos theta-sin theta=sqrt(2)cos theta , then prove that cos theta+sin theta=pm sqrt(2) sin theta .

    Prove that tan(pi//4+theta)-tan(pi//4-theta)=2tan2theta

    Prove that, tan (pi/4 + theta) + tan (pi/4 - theta) = 2 sec 2 theta

    Home
    Profile