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Prove that (cos2theta)/(1+sin2theta)=tan...

Prove that `(cos2theta)/(1+sin2theta)=tan(pi/4-theta)`.

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LHS`(cos2theta)/(1+sintheta)=(cos^2theta-sin^2theta)/(costheta+sintheta)^2=(costheta-sintheta)/(costheta+sintheta)`
`(1-tantheta)/(1+tantheta)=tan(pi/4-theta)`=R.H.S`
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PATHFINDER-MULTIPLE AND SUB-MULTIPLE ANGLES-QUESTION BANK
  1. Prove that (cos2theta)/(1+sin2theta)=tan(pi/4-theta).

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  2. Prove that(1+sintheta-costheta)/(1+sintheta+costheta)="tan"theta/2.

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  3. Prove that sqrt(2+sqrt(2+2cos4theta))=2costheta

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  4. Find the value of cos^2 48^@-sin^2 12^@

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  5. Find the value of sin^2 24^@-sin^2 6^@.

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  6. Find the value of "cos"22 1/2@

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  7. Prove that 8"cos"^3pi/9-6"cos"pi/9=1

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  8. Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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  9. prove that "sin"^4pi/8+"sin"^4(3pi)/8+"sin"^4(5pi)/8+"sin"^4 (7pi)/8=3...

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  10. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

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  11. Prove that "cos" (2pi)/15 cdot "cos"(4pi)/15 cdot "cos" (8pi)/15 "cos...

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  12. Prove that cos^3A+cos^3(120^@+A)+cos^3(240^@+A)=3/4cos3A

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  13. Prove that tanA+tan(60^@+A)-tan(60^@-A)=3tan3A

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  14. Show that cot 7(1^@/2)=2+sqrt2+sqrt3+sqrt6

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  15. Prove that tanAcdottan(A+60^@)+tanAcdottan(A-60^@)+tan(A+60^@)tan(A-60...

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  16. Prove that abs(sinthetasin(60^@-theta)sin(60^@+theta)) le1/4 for all v...

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  17. Prove that if tanA=1/7 and tanB=1/3 then cos2A=sin4B

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  18. Prove that tan6^@tan42^@tan66^@tan78^@=1

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  19. Prove that (1+"cos" (pi)/10)(1+"cos"(3pi)/10)(1+"cos"(7pi)/10)(1+"cos"...

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  20. If sinx=(sqrt5)/3 x lies is the 2nd quadrand then find the value of"c...

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