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If `(1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@)) = 2kcos40^(@)`, then `18k^(4) + 162k^(2) + 369` is divisible by

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ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Single Integer Answer Type Questions)
  1. Find theta (in degree) satisfying the equation,tan 15^@ *tan 25^@* ta...

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  2. The value of "cosec"10^(@)+"cosec"50^(@)-"cosec"70^(@) is

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  3. If cos 5 alpha=cos^5 alpha, where alpha in (0,pi/2) then find the poss...

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  4. tan^2 ((pi)/16) + tan^2 ((2pi)/16) + tan^2((3pi)/16).........+tan^2((7...

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  5. Compute the square of the value of the expression (4+sec 20^@)/(cosec ...

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  6. In DeltaABC, if (sinA)/(3)=(cosB)/(3)=(tanC)/(2), then the value of ...

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  7. It f and g be function defined by f(theta) = cos^2 theta and(theta) = ...

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  8. If sum of the series 1+x log(|(1-sinx)/(cos x)|)((1+sin x)/(cos x))^(1...

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  9. If 9x/costheta+5y/sintheta=56 and 9xsintheta/cos^2theta-5ycostheta/sin...

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  10. The angle A of the DeltaABC is obtuse. x = 2635 - tan B tan C, if [x]...

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  11. If cos3 6^(@)+cot(7 1/2@)=sqrt(n1)+sqrt(n2)+sqrt(n3)+sqrt(n1)+sqrt(n5)...

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  12. If sin^(2)A=x and underset(r=1)overset(4)Pi sin (r A)=ax^(2)+bx^(3)+cx...

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  13. If x,y in Rsatisfies (x+5)^(2)+(y-12)^(2)=(14)^(2) , then the minimum ...

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  14. The least degree of a polynomial with integer coefficient whose one of...

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  15. If A+B+C=180^(@), (sin 2A+sin 2B+sin2C)/(sinA+sinB+sinC)=k sin. (A)/(2...

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  16. The value of f(x)=x^4+4x^3+2x^2-4x+7, when x=cot(11pi)/8 is

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  17. In any DeltaABC, then minimum value of 2020sum(sqrt((sinA)))/((sqrt((s...

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  18. If sintheta+sin^2theta+sin^3theta=1, then prove that cos^6theta-4cos^4...

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  19. 16(costheta-cos(pi/8))(costheta-cos((3pi)/8))(costheta-cos((5pi)/8))(c...

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  20. If (1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@)) = 2kcos40^(@), then 18k^(4...

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