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If a in R, then cos^(2) alpha+cos^(2...

If ` a in R`, then
`cos^(2) alpha+cos^(2)(alpha+2pi//3)+cos^(2)(alpha-2pi//3)` is equal to _____

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The correct Answer is:
`1.50`
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MCGROW HILL PUBLICATION-TRIGONOMETRICAL IDENTITIES AND EQUATIONS -SOLVED EXAMPLES (Numerical Answer Type Questions)
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  2. If 0 lt theta lt pi//2 and sec theta=5//4 then value of (3)/(2) tan ((...

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  3. If 0 lt alpha lt pi//16, then ((tan alpha+2tan(2alpha)+4tan(4alpha)+...

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  4. If theta=pi//9, then log(2)(cos theta)+log(2)(cos 2theta)+log(2)(cos 4...

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  5. sum(k=0)^(11) sec((pi)/(4)+(k pi)/(3)) sec((pi)/(4)+((k+1)pi)/(3)) is ...

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  6. Let alpha= 3pi sum(n=1)^(oo)(1)/(n(n+1)(n+2)(n+3)). Then sqrt(3)[cos a...

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  7. If 0 lt theta lt (pi)/(6), k gt 1 and (tan 3 theta)/(tan theta)=k, the...

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  8. If a in R, then cos^(2) alpha+cos^(2)(alpha+2pi//3)+cos^(2)(alpha-...

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  9. Let alpha=36^(@) and a=sin alpha sin(2alpha) sin(3alpha) sin (4alpha) ...

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  10. Let alpha=pi//8 and a=cos^(8)alpha+cos^(8)(3alpha)+cos^(8)(5alpha)+cos...

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  11. If alpha=pi//11, then cos alpha+cos(3alpha)+cos(5alpha)+cos(7alpha)+...

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  12. "cosec"((pi)/(14))-4cos((2pi)/(7))=

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  13. For theta=pi//7, let P=prod(k=1)^(3)(1-tan^(2)(k theta//2))/(1+tan...

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  14. Let alpha=pi//16, and let S=sin^(4)alpha+sin^(4)(3alpha)+sin^(4)(5a...

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  15. If 12 sin x+5cosx = 2a^(2)-8a+21 has at least one solution, then a is...

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  16. for 0 lt x lt pi, the number of solutions of cos(2x)+cos(4x)+cos(6x)=-...

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  17. If 0 lt x lt 2pi, then the number of solutions of (1+sin x)(sinx)^(cos...

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  18. If 0 lt x lt 12, then the number of solutions of tan((pi)/(6)cos(2pi x...

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  19. Let [x] = greatest integer le x. If -(pi)/(2) lt x lt (pi)/(2), x n...

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  20. Let 0 lt x le y le z lt pi//2. Suppose x, y, z satisfy the following e...

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