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Prove that 2(sin^6theta+cos^6theta)-3(s...

Prove that
`2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0`

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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Solve : abs(x^2+3x)+x^2-2ge0

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  2. Solve : abs(x-1)+abs(x-2)=6

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  3. Prove that 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0

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  4. Show that : 3(sinx-cosx)^4+6(sinx+cosx)^2+4(sin^6x-cos^6x) is indepe...

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  5. If theta lies in the 2^(nd) quadrant and 3 tan theta +4=0, then find t...

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  6. Find the value of tan 105^@

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  7. Prove that tan 70^@=tan 20^@+2tan50^@

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  8. If A + B = 45^@, show that (1+tanA) (1+tanB) =2

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  9. If cos 2x + 2 cosx = 1 then evaluate sin^2x(2-cos^2x)

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  10. Prove that sqrt3 "cosec" 20^@-sec20^@=4

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  11. Prove that : tan A + 2tan2A + 4 tan4A + 8cot8A =cotA

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  12. Evaluate : cos12^@cos24^@cos36^@cos48^@cos72^@cos84^@

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  13. If "coses"theta-sintheta=m,sectheta-costheta=n,"eliminate"theta

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  14. If cos (alpha+beta)=4/5 and sin(alpha-beta)=5/13 and alpha,beta lie be...

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  15. If tan theta=cos theta, where theta in [-pi/2,pi/2], find the number o...

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  16. Find the set of values of theta for which sinthetagtcostheta,, where t...

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  17. Evaluate the following limits : lim(x rarr 0) (sqrt(1+x)-1)/x

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  18. Evaluate the following limits : lim(x rarr 0) (sin3x+7x)/(4x+sin2x)

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  19. Evaluate the following limits : lim(x rarr 0) (1-cosx)/((e^(x^2)-1))

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  20. Evaluate the following limits : lim(xrarrpi/2)(pi/2-x)tanx

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