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If "coses"theta-sintheta=m,sectheta-co...

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`"coses"theta-sintheta=m,sectheta-costheta=n,"eliminate"theta`

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If cosectheta-sintheta=m" and " sectheta-costheta=n , elimnate theta .

Prove the following identities: (cosec theta-sintheta)^2+(sectheta-costheta)^2-(tantheta-cottheta)^2=1

. Let f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(sinthetacostheta,sin^2theta,costheta),(sintheta,-costheta,0):}|,"find" f(pi/3) .

If A = [(costheta,-sintheta),(sintheta,costheta)] , then the matrix A^(-50) , when theta = (pi)/(12) , is equal to

Evalute : |{:(cos^2 theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta,0):}|

If f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta," "0):}| , then find the value of f((pi)/6) .

If tan theta+sin theta=m and tan theta-sin theta=n , then

If A=[(costheta,sintheta),(-sintheta,costheta)] , then prove that A^(n)=[(cosntheta,sin n theta),(-sin ntheta,cos n theta)], n in N .

Simplify costheta[(costheta,sin theta),(-sintheta,costheta)]+sin[(sintheta,-costheta),(costheta,sintheta)]

The solution of the equation |(costheta,sintheta,costheta),(-sintheta,costheta,sintheta),(-costheta, -sintheta,costheta)|=0 is -

PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Prove that : tan A + 2tan2A + 4 tan4A + 8cot8A =cotA

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Find the derivative of the following functions w.r.t.x: (tanx)^(x)

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  18. Find the derivative of the following functions w.r.t.x: y=sin 2x + e...

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  19. Find the derivative of the following functions w.r.t.x: y=log (1+x^3...

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  20. Find the derivative of the following functions w.r.t.x: y=e^(4x)/x^2

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