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If cos4x=a0+a1cos^2x+a^2cos^4x is true f...

If `cos4x=a_0+a_1cos^2x+a^2cos^4x` is true for all values of `x in R ,` then the value of `5a_0+a_1+a_2` is_______

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The correct Answer is:
5
`cos 4x=2 cos^(2) 2x-1`
`=2(2 cos^(2) x-1)^(2)-1`
`=2(4 cos^(4) x+1-4 cos^(2) x)-1`
`=8 cos^(4) x-8 cos^(2) x+1`
`:. a_(0)=1, a_(1)=-8, a_(2)=8`
`:. 5a_(0)+a_(1)+a_(2)=5`
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CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Numerical)
  1. If log(0.5) sin x=1-log(0.5) cos x, then the number of solutions of x ...

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  2. Number of roots of the equation (3+cos"x")^2=4-2sin^8x ,x in [0,5pi]a ...

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  3. Number of solutions (s) of the equation (sin x)/(cos 3x) +(sin 3x)/(co...

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  4. Number of solutions of the equation (sqrt(3)+1)^(2x)+(sqrt(3)-1)^(2x)=...

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  5. Number of integral value(s) of m for which the equation sinx-sqrt(3)co...

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  6. The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi...

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  7. If cos4x=a0+a1cos^2x+a^2cos^4x is true for all values of x in R , the...

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  8. Number of integral values of a for which the equation cos^2x-sinx+a=0 ...

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  9. Number of roots of the equation 2^(tan(x-pi/4))-2(0. 25)^sin^(3((x-pi/...

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  10. The number of solution of sin^(4)x-cos^(2) x sin x+2 sin^(2)x+sin x=0 ...

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  11. Let k be sum of all x in the interval [0,2pi] such that 3cot^2x+8cotx+...

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  12. If theta in [0,5pi]a n dr in R such that 2sintheta=r^4-2r^2+3 then th...

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  13. If 2tan^2x-5secx=1 is satisfied by exactly seven distinct values of x ...

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  14. If sinx+siny geq cosa cosx, AA x in R then siny+cos a=

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  15. If sin(sinx+cosx)=cos(cosx-sinx), and largest possible value of sinxi ...

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  16. The number of solutions of the equation 1+cosx+cos2x+sinx+sin2x+sin3x=...

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  17. the least value of 'a' for which the equation 2sqrt(a) sin^(2) x+sqrt(...

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  18. The number of ordered pair (x, y) satisfying the equation sin^(2) (x+y...

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  19. Total no. of orderd pairs (x,y) satisfying x(sin^2 x+ 1/x^2)=2sinx,si...

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  20. Number of solutions of the equation cos 5x xx tan (6|x|)+sin 5x=0 lyin...

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