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Prove that sinx/cos(3x)+sin(3x)/cos(9x)+...

Prove that `sinx/cos(3x)+sin(3x)/cos(9x)+sin(9x)/cos(27x)=1/2 (tan27x-tanx)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. If sinA=4/5 and cosB=5/(13),where 0ltAltpi/2 ;0ltBltpi/2 , find the ...

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

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

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

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

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  7. If tanA=3/4,cosB=9/(41), where pi lt A lt (3pi)/2 and 0 lt B lt pi/2 ...

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  8. If sinA=1/2,cosB=(12)/(13), w h e r e pi < A < (3pi)/2 and (3pi)/2...

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  9. If sinA=1/2,cosB=(sqrt(3))/2, where pi/2 lt A lt pi and 0 lt B lt ...

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  10. If sinA=1/2,cosB=(sqrt(3))/2, w h e r epi/2 lt A lt pi and 0ltBltpi/2...

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  11. Evaluate the following: sin 78^0cos 18^0-cos 78^0sin 18^0

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  12. Evaluate the following: sin 36^0cos9^0+cos36^0 sin9^0

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  13. Evaluate the following: cos 47^0cos 13^0-sin 47^0 sin 13^0

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  14. Evaluate the following: cos 80^0cos 20^0+ sin 80^0 sin 20^0

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  15. If cos A=-12/13 and cotB=24/7 where A lies in second quadrant and B li...

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  16. Prove that: cos 105^@+cos15^@=sin 75^@-sin 15^@

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  17. Prove that: (tanA+tanB)/(tanA-tanB)=sin(A+B)/(sin(A-B)

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  18. Prove that: (cos 11^@+"sin"11^@)/(cos 11^@-"sin"11^@)=tan 56^@

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  19. Prove that: (cos8^@+"sin"8^@)/(cos8^@-"sin"8^@)=t a n 53^@

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  20. The value of : (cos9^@+sin9^@)/(cos9^@-sin9^@) is:

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