Home
Class 12
MATHS
If 0ltxltpi/4andcosx+sinx=3/5, then the ...

If `0ltxltpi/4andcosx+sinx=3/5`, then the value of `25(cosx-sinx)^2` is ___________ .

Text Solution

Verified by Experts

The correct Answer is:
7
Let `y=cosx-sinx(ygt0)`
`y^2=1-2 sinx.cosx`
`cosx+sinx=5/4 ("Given")`
`:. 1+2 sinxcosx=25/16`
`or 2sinx.cosx=9/16`
Now `y^2=1-2sinxcosx=1-9/16=7/16`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Archives JEE Main|2 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Archives JEE Advanced single correct answer type|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Matrix Match Type|3 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

If 0 lt x lt 5/4 and cosx+sinx=5/4 then the value of 16(cosx-sinx)^2 is

If 2cosx+sinx=1, then find the value of 7cosx+6sinxdot

The value of int(dx)/(cosx-sinx) is equal to -

The maximum value of cos^2(45^0+x)+(sinx-cosx)^2 is ______

The minimum value of 2^(sinx)+2^(cosx) is -

The value of f(x)=sinx+cosx at x=45^@ is

Find the derivative of (x^(5)-cosx)/(sinx)

The minimum value of ((3sin x-4cosx-10)(3sinx+4cosx-10)) is ________

cot2x = cosx + sinx

If I=int_0^((3pi)/4)[(1+x)sinx+(1-x)cosx]dx , then value of (sqrt(2)-1)I is_____