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If 4sin^4x+cos^4x=1,t h e nxi se q u a l...

If `4sin^4x+cos^4x=1,t h e nxi se q u a lto(n in Z)` `npi` (b) `npi+-sin^(-1)sqrt(2/5)` `(2npi)/3` (d) `2npi+-pi/4`

A

`n pi`

B

`npi pm sin^(-1) sqrt(2/5)`

C

`(2 n pi)/3`

D

`2n pi pm pi/4`

Text Solution

Verified by Experts

The correct Answer is:
A, B
We have `4 sin^(4)x+cos^(4)x=1`
or `4 sin^(4)x=1-cos^(4)x`
`=(1-cos^(2) x) (1+ cos^(2) x)`
`=sin^(2) x (2-sin^(2) x)`
or `sin^(2)x[5 sin^(2) x-2]=0`
or `sin x=0` or `sin x= pm sqrt(2//5)`
`rArr x=n pi` or `x=n pi pm sin^(-1) sqrt(2/5), n in Z`
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CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Multiple)
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  2. If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1, then theta is e...

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  3. A general solution of tan^(2) theta+ cos 2 theta=1 is (n in Z)

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  4. If sinx+cosx=sqrt(y+1/y) for x in [0,pi] , then x=pi/4 (b) y=0 y=1 ...

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  5. The equation 2 sin^(2) (pi/2 cos^(2) x)=1-cos (pi sin 2x) is safisfied...

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  6. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

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  7. For the smallest positive values of xa n dy , the equation 2(s inx+s i...

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  8. For the equation 1-2x-x^2=tan^2(x+y)+cot^2(x+y) exactly one value of ...

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  9. If x+y=pi//4 and tan x+tan y=1, then (n in Z)

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  10. If x+y=2pi//3 and sin x//sin y=2, then the

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  11. Let tanx-tan^2x >0 and |2s inx|<1 . Then the intersection of which of ...

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  12. If cos(x+pi/3)+cos x=a has real solutions, then number of integral val...

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  13. If 0 le x le 2pi, then 2^(cosec^(2) x) sqrt(1/2 y^(2) -y+1) le sqrt(2...

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  14. If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, p...

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  15. If (cos e c^2theta-4)x^2+(cottheta+sqrt(3))x+cos^2(3pi)/2=0 holds true...

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  16. If (sinalpha)x^2-2x+bgeq2, for all real values of xlt=1a n dalpha in (...

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  17. The value of x in (0,pi/2) satisfying the equation, (sqrt3-1)/sin x+ (...

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  18. If cos3theta=cos3alpha, then the value of sintheta can be given by +-s...

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  19. Which of the following sets can be the subset of the general solution ...

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  20. The values of x1 between 0 and 2pi , satisfying the equation cos3x+cos...

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