Home
Class 11
MATHS
If 3tan(theta-15^0)=tan(theta+15^0), the...

If `3tan(theta-15^0)=tan(theta+15^0),` then `theta` is equal to `n in Z)`

A

n`pi+pi/4`

B

`npi+pi/8`

C

`npi+pi/3`

D

none of these

Text Solution

Verified by Experts

`3tan(theta-15^@) = tan(theta+15^@)`
`=>(tan(theta+15^@))/(tan(theta-15^@)) = 3/1`
Using componendo and dividendo,
`=>(tan(theta+15^@)+tan(theta-15^@))/(tan(theta+15^@)-tan(theta-15^@)) = (3+1)/(3-1)`
`=>(sin(theta+15^@)/cos(theta+15^@)+sin(theta-15^@)/cos(theta-15^@))/(sin(theta+15^@)/cos(theta+15^@)-sin(theta-15^@)/cos(theta-15^@)) = 2`
`=>(sin(theta+15^@)cos(theta-15^@)+sin(theta-15^@)cos(theta+15^@))/(sin(theta+15^@)cos(theta-15^@)-sin(theta-15^@)cos(theta+15^@)) = 2`
`=>(sin(theta+15^@+theta-15^@))/(sin(theta+15^@-theta+15^@)) = 2`
`=>(sin2theta)/(sin30^@) = 2`
...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

3tan(theta - pi/12) = tan(theta + pi/12)

If tan 2theta . Tan 3 theta =1 , then sin5theta =

Knowledge Check

  • If m tan (theta -30^(@)) = n tan (theta +120^(@)), then the value of cos 2 theta is -

    A
    `(m+n)/(2(m-n))`
    B
    `(m+n)/(m-n)`
    C
    `(m-n)/(m+n)`
    D
    `(2m-n)/(2(m+n))`

  • If tan2theta=cos(theta+15^(@)) then the value of theta is

    A
    `5^(@)`
    B
    `10^(@)`
    C
    `20^(@)`
    D
    `25^(@)`

  • If sec theta + tan theta = x,then tan theta is

    A
    `((x^2+1))/x`
    B
    `((x^2-1))/x`
    C
    `((x^2+1))/(2x)`
    D
    `((x^2-1))/(2x)`

    • Similar Questions

    Explore conceptually related problems

    If tan(theta+15^@)= sqrt3 then sin theta+ cos theta =?

    tan3theta + tantheta = 2tan 2theta

    If tan theta=-4/3 ,then the value of sin theta is

    If cot theta =tan (n-1) theta then the value of theta will be

    If theta be an angle and sin(10 theta)= cos (5theta-15^0) then the value of theta is

    Home
    Profile