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If tantheta+sintheta=mandtantheta-sinthe...

If `tantheta+sintheta=mandtantheta-sintheta=n`,then

A

`m^2-n^2=4mn`

B

`m^2+n^2=4mn`

C

`m^2-n^2=m^2+n^2`

D

`m^2-n^2=4sqrt(mn)`

Text Solution

Verified by Experts

The correct Answer is:
D
From the given relations,
`m+n=2tantheta,m-n=2sintheta`.
Thus,`m^2-n^2=4tanthetasintheta`
Also `sqrt(mn)=sqrt(tan^2theta-sin^2theta)=sinthetatantheta`
From Eqs. (i) and (ii), we get `m^2-n^2=4sqrt(mn)`.
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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. If tantheta =-4/3," then " costheta is

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  2. If cosx+secx=2," then "cos^nx+sec^nx is equal to

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  3. If tantheta+sintheta=mandtantheta-sintheta=n,then

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  4. If cosectheta+cottheta=m, then the value of cosectheta is

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  5. If (sinx)/a=(cosx)/b=(tanx)/c=k , then b c+1/(c k)+(a k)/(1+b k) is eq...

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  6. If sec^4theta+sec^2theta=10+tan^4theta+tan^2theta", then "sin^2theta=

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  7. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

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  8. If secalpha and cosecalpha are the roots of the equation x^2-px+q=0, t...

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  9. Which of the following is not the quadratic equation whose roots are c...

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  10. If sinx+sin^2x=1n then the value of cos^12x+3cos^10x+3cos^8x+cos^6x-1 ...

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  11. 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)...

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  12. If secx+sec^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

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  13. (1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=

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  14. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

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  15. A circle is drawn in a sector of a larger circle of radius r , as show...

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  16. A right triangle has perimeter of length 7 and hypotenuse of length 3....

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  17. Given that the side length of a rhombus is the geometric mean of the ...

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  18. Which of the following is correct?

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

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  20. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

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