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If the quadratic equation 4^(sec^(2)al...

If the quadratic equation
`4^(sec^(2)alpha)x^(2)+2x+(beta^(2)-beta+1/2)=0` have real roots, then find all the possible values of `cos alpha+cos^(-1)beta`.

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The correct Answer is:
`cos alpha-cos^(-1)beta={:{(pi/3-1",when n is an even integar"),(pi/3+1",when n is an even integer"):}`
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ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Subjective Type Questions)
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  2. The set of values of a for which the equation Sin^4 x + Cos^4 x = a ha...

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  3. If a and b are positive quantities, (a gt b) find minimum positive val...

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  4. If a, b, c and k are real constants and alpha, beta, gamma are variab...

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  5. If x/("tan"(theta+alpha))=y/("tan"(theta+beta))=z/(tan(theta+gamma)), ...

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  6. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...

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  7. Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...

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  8. If {sin ( alpha-beta)+cos(alpha+2beta)sin beta}^(2)=4 cos alpha sin be...

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  9. If A, B, C are the angle of a triangle and |(sinA,sinB,sinC),(cosA,...

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  10. In any DeltaABC, prove that Sigma (sqrt(sinA))/(sqrt(sinB)+sqrt(sinC...

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  11. If 2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0, prove tha...

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  12. If the quadratic equation 4^(sec^(2)alpha)x^(2)+2x+(beta^(2)-beta+1/...

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  13. If cos2theta=x+1/x, prove that 2cos3theta=x^3+1/x^3

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  14. If (cos theta(1))/(cos theta(2))+(sin theta(1))/(sin theta(2))=(cos th...

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  15. Prove that sum(k=1)^(n-1) ""^(n)C(k)[cos k x. cos (n+k)x+sin(n-k)x.s...

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  16. Determine all the values of x in the interval x in [ 0, 2pi] which sat...

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  17. Total number of solution for the equation x^(2)-3[sin(x-(pi)/6)]=3 is ...

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  18. In aDeltaABC, prove that Sigma(r=0)^(n)""^(n)C(r)a^(r)b^(n-r) cos ( ...

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  19. Resolve Z^5+ 1 into linear & quadratic factors with real coefficients...

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  20. Prove that the roots of the equation 8x^(2)-4x^(2)-4x+1=0 are cos. (...

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