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Prove that (tan(pi/4+x))/(tan(pi/4-x))=(...

Prove that `(tan(pi/4+x))/(tan(pi/4-x))=((1+t a n x)/(1-t a n x))^2`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. Prove that: cos((3pi)/4+x)-cos((3pi)/4-x\ )=sqrt(2)sinx

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  2. Prove that: sin(x+y)/sin(x-y)=(tanx+tany)/(tanx-tany)

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  3. Prove that (tan(pi/4+x))/(tan(pi/4-x))=((1+t a n x)/(1-t a n x))^2

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  4. if tanalpha=1/(sqrt(x(x^2+x+1))), tanbeta=(sqrtx)/(sqrt(x^2+x+1) and ...

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  5. Prove that :(tan(A+B))/("cot"(A-B))=(sin^2A-sin^2B)/(cos^2A-sin^2B)

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  6. Prove that : sin^2 6x-sin^2 4x=sin 2x\ sin\ 10 x

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  7. Prove that: cos^2 2x-cos^2 6x= sin4x sin8x

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  8. Prove that: (cos^2 33^@-cos^2 57^@)/(sin^2(21/2)^@-sin^2(69/2)^@)=-sqr...

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  9. Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=co...

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  10. Prove that: t a n 70^0=t a n 20^0+2t a n 50^0dot

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  11. If sin alpha+sin beta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  12. If sin alpha+sin beta=a\ a n d\ cosalpha+cosbeta=b , show that : sin(a...

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  13. If sinA=4/5 and cosB=5/13, find the value of the following : "sin"(A+B...

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  14. If sinA=4/5 and cosB=5/(13), where 0 < A,B < pi/2 ,find the value of...

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  15. If sinA=4/5 and cosB=5/(13),where 0ltAltpi/2 ;0ltBltpi/2 , find the ...

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  16. If sinA=4/5 and cosB=5/(13),where 0ltAltpi/2 ;0ltBltpi/2 , find the ...

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  17. If sinA=12/13 and sinB=4/5 where pi/2 < A < pi and 0 < B < pi/2 then f...

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  18. Prove that sinx/cos(3x)+sin(3x)/cos(9x)+sin(9x)/cos(27x)=1/2 (tan27x-t...

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  19. If sin A=3/5, cos B=-(12)/(13),\ w h e r e A and B both lie in second ...

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  20. If cosA=-24/25 and cos B=3/5 where pi < A < (3pi)/2 and (3pi)/2 < B < ...

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