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If tan(picostheta)=cot(pisintheta) Prove...

If `tan(picostheta)=cot(pisintheta)` Prove that `sin(theta+pi/4)=1/(2sqrt2)`

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PATHFINDER-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-QUESTIONBANK
  1. Evaluate:"sin"pi/4"cos"pi/(12)+"cos"pi/4"sin"pi/(12)

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  2. (tan ((pi)/(4) +x))/( tan ((pi)/(4) -x ))= ((1 + tan x )/( 1- tan x ))...

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  3. Prove that sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt2sinA

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  4. Find the value of tan15^@

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  5. Prove that sin^2(n+1)A-sin^2nA=sin(2n+1)AsinA

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  6. If tan(A+B)=x and tan(A-B)=y find the value of tan2A.

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  7. If log(b) n = 2 and og(n) 2b = 2, then find the value of b.

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  8. Prove that (tan69^@+tan66^@)/(1-tan69^@tan66^@)=-1.

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  9. If tanA=5/6 and tanB=1/(11), Prove that A+B=pi/.4

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  10. Prove that sin^2B=sin^2A+sin^2(A-B)-2sinAcosBsin(A-B)

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  11. Prove that cos^2A+cos^2B-2cosAcosBcos(A+B)=sin^2(A+B).

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  12. Prove that tan8theta-tan6theta-tan2theta=tan8thetatan6thetatan2theta.

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  13. If tanA+tanB=a and cotA+cotB=b.Prove that cot(A+B)=1/a-1/b

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  14. If tanx+tan(x+pi/3)+tan(x+(2pi)/3)=3 then prove that (3tanx-tan^3x)/(1...

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  15. cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalp...

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  16. If tan(picostheta)=cot(pisintheta) Prove that sin(theta+pi/4)=1/(2sqrt...

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  17. Let tan alpha = a/(a+1) and tan beta =1/(2a +1), then alpha + beta is:

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  18. If theta lies in the 1st quadrant and costheta=8/(17) then prove that ...

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  19. If alpha, beta are the solutions of the equation a tantheta+b secthet...

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  20. Prove that tan70^(@)=2tan50^(@)+tan20^(@).

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