Home
Class 12
MATHS
Find the smallest positive root of the e...

Find the smallest positive root of the equation `sqrt(sin(1-x))=sqrt(cos"x")`

Text Solution

Verified by Experts

The given equation is possible if `sin(1-x) ge 0` and `cos x ge 0`. On squaring, we get `sin(1-x)=cos x`
or `cos (pi/2-(1-x))=cos x`
`rArr pi/2-1+x=2npi pm x, n in Z`
or `x=(2npi-pi/2+1)/2, n in Z`
For `n=2, x=(7pi)/4+1/2`, which is the smallest positive root of the given equation.
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|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

If alpha be the smallest positive root of the equation sqrt(sin(1-x))=sqrt(cos x) , then the approximate integeral value of alpha must be .

the roots of the equation sqrt(3x+1)+1=sqrt(x) are

13.The roots of the equation x^(sqrt(x))=(sqrt(x))^(x)

Solve the equation sqrt(3)cos x+sin x=sqrt(2)

Find the product of the positive roots of the equation sqrt((2008)(x))^((log)2008^(x))=x^(2)

Determine the smallest positive value of x which satisfy the equation sqrt(1+sin2x)-sqrt(2)cos3x=0

The number of distinct real roots of the equation sqrt(sin x)-(1)/(sqrt(sin x))=cos x("where" 0le x le 2pi) is

Find the product of the positive roots of the equation sqrt(2017)(x)^(log_(017)x)=x^(2)

Find the product of the positive roots of the equation sqrt2009(x)^(log_(2009)(x))=x^2 .