Home
Class 12
MATHS
The equation 2cos^2(x/2)sin^2x=x^2+x^(-2...

The equation `2cos^2(x/2)sin^2x=x^2+x^(-2);0 <= x <=pi/2` has

Text Solution

Verified by Experts

The given equation is
`2 cos^(2) (x/2) sin^(2) x=x^(2) +1/x^(2)`
where `0 lt x le pi/2`
`LHS=2 cos^(2) (x/2) sin^(2) x=(1+cos x) sin^(2)x`
`:' 1+cos x lt 2 and sin^(2) x le 1` for `0 lt x lt pi/2`
`:. (1+ cos x) sin^(2) x lt 2`
Also, `R.H.S.=x^(2) +1/x^(2) ge 2`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

Solve the equation sin^4x+cos^4x-2sin^2x+(3sin^2 2x)/4=0

Solve the equation 2(cos x+cos2x)+sin2x(1+2cos x)=2sinx for (-pilt=xlt=pi)

The number of distinct real roots of the equation sin^(3)x +sin^(2)x sin x-sin x- sin 2x-2cos x=0 belonging to the interval (-(pi)/(2),(pi)/(2))

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .

(cos2x)/(sin ^(2) x cos^(2) x)

The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

Find common roots of the equations 2sin^2x+sin^2 2x=2a n dsin2x+cos2x=tanxdot

The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi/6)dotcospi/6=sin^2pi/6 in interval ((-pi)/2,pi/2) is_________

The number of distinct solutions of the equation 5/4cos^(2)2x + cos^4 x + sin^4 x+cos^6x+sin^6 x =2 in the interval [0,2pi] is