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If cos 2x + 2 cosx = 1 then evaluate sin...

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

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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Prove that tan 70^@=tan 20^@+2tan50^@

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Evaluate the following limits : lim(xrarr0)[(sqrt(1+2x)-sqrt(1-2x))/...

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  16. Evaluate the following limits : lim(xrarr2) (x^(7/3)-2^(7/3))/(x-2)

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  17. lim(x to 0) (1-cosx)/x^2 = ?

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  18. Find the derivative of the following w.r.t.x: In sqrt((x^2+x+1))

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  19. Find the derivative of the following functions w.r.t.x: cos (In x)

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  20. Find the derivative of the following functions w.r.t.x: e^(2x)/(In x...

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