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Let alpha=pi//10, then sin alpha sin (3a...

Let `alpha=pi//10`, then `sin alpha sin (3alpha)=`_________

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MCGROW HILL PUBLICATION-TRIGONOMETRICAL IDENTITIES AND EQUATIONS -EXERCISE (Numerical Answer Type Questions)
  1. If tan theta+cot theta=4, then tan^(4) theta+cot^(4) theta=

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  2. Suppose 0 lt theta lt pi//2. If a sin^(3)theta+b cos^(3) theta=sin the...

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  3. Let alpha=pi//10, then sin alpha sin (3alpha)=

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  4. Let theta=pi//5, then 4|cos theta cos (2 theta) cos(4 theta) cos (8 th...

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  5. Let theta=pi//6, and a=(1+cos theta)(1+cos 2theta)(1+cos 4 theta) (1+c...

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  6. If 0 lt a lt 1, then log(a)(tan 1^(@))+log(a)(tan 2^(@))+… + log(a)(ta...

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  7. 4 sin((pi)/(18))sin((5pi)/(18))sin((7pi)/(18))=

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

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

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

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

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

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

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

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

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

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

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

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

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

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