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If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos...

If `(sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4`, then the value of `2 tan^(2)x` is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`(sin^(2)x-2soc^(2)x + 1)/(sin^(2)x+2cos^(2)x-1)=4`
`rArr sin^(2)x-2 cos^(2)x+1`
`=4 sin^(2)x +8 cos^(2)x-4`
`rArr 10 cos^(2)x+3 sin^(2)x-5=0`
`rArr 10+3tan^(2)x-5(1+tan^(2)x)=0`
`rArr 2 tan^(2)x=5`
`therefore tan^(2)x=(5)/(2)`
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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  2. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  3. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

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  4. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  5. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

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  6. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

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  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  8. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  10. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

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  11. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

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  12. Which of the following is true ?

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  13. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

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  14. Which of the following is greatest ?

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  15. The number of value/values of x for which sin y=x^(2)-2x si possible i...

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  16. Which of the following is not correct ?

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  17. If sin^(4)alpha+cos^(4)beta+2=4 sin alpha cos beta, 0 le alpha, (pi)/(...

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  18. Number of ordered pairs (a, x) satisfying the equation sec^2(a+2)x+a^2...

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  19. Find the range of y=sin^3x-6sin^2x+11sinx-6.

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  20. Let f(x)=a sin x+c, where a and c are real numbers and a>0. Then f(x)l...

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