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Let a(n)=sum(k=1)^(n)tan^(-1)((2^(k))/(2...

Let `a(n)=sum_(k=1)^(n)tan^(-1)((2^(k))/(2+4^(k)))`, then `tan(a(oo)-a(2))` is equal to ________

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`0.25`
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MCGROW HILL PUBLICATION-TRIGONOMETRICAL IDENTITIES AND EQUATIONS -EXERCISE (Numerical Answer Type Questions)
  1. 4 sin((pi)/(18))sin((5pi)/(18))sin((7pi)/(18))=

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  2. If cot (theta-alpha) cot(theta-beta)=cot^(2) theta, then 2(1+cot(2the...

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  3. If alpha=(pi)/(28), and a=(sin alpha)/(cos(3alpha))+(sin (3alpha))/(c...

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  4. Let alpha=pi//12 , and E=(1+cos alpha)(1+cos(3alpha))(1+cos(5alpha))(1...

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  5. Suppose f(theta)=cos theta cos(2theta) cos(2^(2) theta)-cos(2^(n) t...

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  6. For theta in R, let f(theta)=cos^(2)theta+cos^(2)(theta+pi//6)+sin...

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  7. Let a(n)=sum(k=1)^(n)tan^(-1)((2^(k))/(2+4^(k))), then tan(a(oo)-a(2))...

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  8. If (sin^(2)x)/(1+sin^(2)x)+(cos^(2)x)/(1+cos^(2)x)=2+(k)/(cos(4x)-17) ...

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  9. (tan 10^(@)+tan 70^(@)-tan50^(@))^(2)= .

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  10. tan^(6)((pi)/(9))-33 tan^(4)((pi)/(9))+27tan^(2)((pi)/(9))= .

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  11. Let f(x)=cos^(2)((pi)/(4)+x)+(sinx-cosx)^(2), AA x in R then max(f(x))...

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  12. Let M = the maximum value of (1)/(9 sin^(2)x+24 sin x cosx+19cos^(2...

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  13. Let alpha=(1)/(8) sum(k=0)^(10)sec((7pi)/(12)+(kpi)/(2)) sec((7pi)/(12...

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  14. Suppose for 0 lt x lt (pi)/(2), (sin(7x))/(sinx)=a cos(6x)+b cos(4x)+c...

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  15. If x in [0, 2pi], then the number of solutions of sin^(5)x-cos^(5)x=(1...

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  16. If x in [0, 2pi], then the number of solutions of sin^(3)x+cos^(3)x=1,...

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  17. If x in [0, 2pi], then the number of solutions of 4-4(cosx-sin x)-sin2...

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  18. The number of solutions of 2(cosx+cos(2x))+sin(2x)(1+2cosx)=2sinx lyin...

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  19. The number of solutions of tanx tan(x+pi//3)tan(x+2pi//3)= -1 lying...

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  20. The number of values of x in (0, 2pi) satisfying the equation |cosx|^(...

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