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If a cos^3theta +3a cos theta sin^2theta...

If a `cos^3theta +3a cos theta sin^2theta =x` and `asin^3theta+3a cos^2theta sin theta=y` prove that `(x+y)^(2/3)+(x-y)^(2/3)=2a^(2/3)`

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PATHFINDER-TRIGONOMETRIC RATIOS AND IDENTITIES-QUESTION BANK
  1. Show that (sin^2 theta)/(1-cot theta)+(cos^2 theta)/(1-tan theta )=1+s...

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  2. If a sec alpha +btan alpha=d and bsec alpha +a tan alpha=c prove that ...

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  3. If a cos^3theta +3a cos theta sin^2theta =x and asin^3theta+3a cos^2th...

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  4. If cos alpha =1/2(x+1/x),cos beta=1/2(y+1/y) then evaluate cos(alpha-b...

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

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  6. Prove that sqrt3cosec 20^@-sec20^@=4

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  7. Without using tables prove that (sin12^@)(sin 48^@)(sin 54^@)=1/8

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  8. In any triangle prove that cot(A/2)+cot (B/2)+cot(C/2)=cot(A/2)cot(B/2...

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  9. Find the value of (1+cos (pi/8))(1+cos(3pi/8))(1+cos(5pi/8))(1+cos(7pi...

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  10. Find the value of (sqrt((1+sin 2A))+sqrt(1-sin 2A))/(sqrt(1+sin 2A)-sq...

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  11. Find the maximum and minimum value of 6sinx cosx +4cos2x

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  12. If f(x)=(sin3x)/sin x,X ne n pi then find range of f(x)

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  13. Find the maximum and minimum value of cos^2theta -6 sin theta .cos the...

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  14. Prove that sin 6^@ sin 42^@sin 66^@sin 78^@=1/16

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  15. if 0ltalpha,beta,gamma lt(pi/2) prove that sin alpha+sin beta+sin gamm...

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  16. Show that sin(pi/n)+sin (3pi/n)+sin (5pi/n)+….n terms=0

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  17. .(tantheta +sectheta-1)/(tantheta -sectheta+1)=

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  18. If sectheta=sqrt2 and (3pi)/2ltthetalt2pi. Then the value of (1+tanthe...

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  19. (cosec(2pi+theta)cos(2pi+theta)tan(pi/2+theta))/(sec(pi/2+theta)costhe...

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  20. In triangle ABC, right angled at C, (tanA+tanB) equal to

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