Home
Class 11
MATHS
If cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2...

If `cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2x` is equal to

Text Solution

Verified by Experts

GIven `cos2x+2cosx=1`
=`2cos^2x-1+2cosx=1`
=`2cos^2x+2cosx=1+1`
=`2cos^2x+2cosx=2`
=`cos^2x+cosx=1........(i)`
Now as given`(2-cos^2x)sin^2x` =`(2-cos^2x)(1-cos^2x)` =`(2-(1-cosx))(1-(1-cosx))`[by equation (i)] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

If cos2x+2cos x=1 then (2-cos^(2)x)sin^(2)x is equal to

If cos2x+2 cos x=1 , then (sin^(2)x)(2-cos^(2)x) is equal to

Knowledge Check

  • int 1/(sin^2x cos^2x )dx is equal to:

    A
    `tanx+cotx+c`
    B
    `tanx-cotx+c`
    C
    `tanx.cotx+c`
    D
    `tanx-cot2x+c`

  • int(sin(2x))/(1+cos^2x)dx is equal to

    A
    `-1/2log(1+cos^2x)+C`
    B
    `2log(1+cos^2x)+C`
    C
    `1/2log(1+cos2x)+C`
    D
    `C-log(1+cos^2x)`

  • int (sin^2x-cos^2x)/(sin^2x cos^2 x) dx is equal to:

    A
    tanx+cotx+c
    B
    tanx+cosecx+c
    C
    `-tanx+cotx+c`
    D
    `tanx+secx+c`

    • Similar Questions

    Explore conceptually related problems

    If cos2x+2cos x=1 then sin^(2)x(2-cos^(2)x) is

    If cos2x+2cos x=1 then sin^(2)x(2-cos^(2)x) is

    if sin x=cos^(2)x then cos^(2)x(1+cos^(2)x) is equal to

    If 2sin x-cos2x=1 ,then (cos^(2)x+cos^(4)x+4)/(2) is equal to

    If tan x + cot x =2 , then sin^(2n)x + cos^(2n) x is equal to

    Home
    Profile