Home
Class 11
MATHS
If cos3x+sin(2x-(7pi)/6)=-2 , then show ...

If `cos3x+sin(2x-(7pi)/6)=-2` , then show that x is of the form π / 3(6n+1) .

Text Solution

Verified by Experts

`cos3xx+sin(2x-7/5pi)=-2`
`1+cos3x+1+sin(3x-7/6pi)=0`
`2cos^2 3/2x+1+sin(3x-2/3pi-pi/2)=0`
`2cos^2(3/2x)+1-sin(pi/2-(-3x+2/3pi))=0`
`2cos^2(3/2x)+1-cos(2/3pi-2x)=0`
`2cos^2(3/2x)+2sin^2(pi/3-x)=0`
`cos3/2x=0,sin(pi/3-x)=0`
`3/2x=pi/2,3/2pi,5/2pi,7/2pi...`
...
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

If cos^-1(x/2)+sin^-1(x/4)=pi/6 , then the value of x is

For 0

Knowledge Check

  • If sin^-1 x - cos^-1 x = pi/6 then x is

    A
    44198
    B
    `sqrt3/2`
    C
    -0.5
    D
    none of these

  • If sin^-1x+sin^-1y=(2pi)/3 , then cos^-1x+cos^-1y =

    A
    `(2pi)/3`
    B
    `pi/3`
    C
    `pi/6`
    D
    `pi`

  • If sin x + sin ^(2)x =1, then the value of (cos ^(12) x+ 3 cos ^(10) x +3 cos ^(8) x+ cos ^(6)x) is-

    A
    1
    B
    4
    C
    2
    D
    3

    • Similar Questions

    Explore conceptually related problems

    If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48cos^2x))sinx)=x-cos^(-1)(7cosx)

    If x in (0,pi//2)a n dcosx=1//3 , then prove that sum_(n=0)^oo(cosn x)/(3^n)=(3(3-cosx))/(10-6cosx+cos^2x)

    "If " (tan x)/(tan y) = (1 + cos^(2) x)/(1 + sin^(2) x ) " show that "sin ( 3x + y) =7sin (x-y).

    If x=2^(2/3)+2^(1/3) show that x^(3)-6x=6

    For all x in 0 le x le (pi)/(2) , show that, cos(sin x) > sin(cos x)

    Home
    Profile