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Prove that: (sinx)/(cos3x)+(sin3x)/(cos...

Prove that: `(sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(tan27 x-tanx)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. If cotalpha=1/2,secbeta=-5/3,where piltalphalt(3pi)/2and pi/2 ltbetalt...

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  2. If sin A=3/5,0<A<pi/2a n dcosB=(-12)/(13),0<B<(3pi)/2, find the follow...

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  3. Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(ta...

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  4. Prove that: 1/(cos(x-a)cos(x-b))=(tan(x-b)-"tan"(x-a))/(sin(a-b))

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  5. If sin(picostheta)=cos(pi sintheta),t h e n sin2theta=

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  6. If at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2) , where alpha!=beta...

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  7. Prove that: 1/(sin(x-a)sin(x-b))=(cot(x-a)-"cot"(x-b))/(sin(a-b))

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  8. If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi ...

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  9. If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that si...

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  10. Prove that: 1/(sin(x-a)cos(x-b))=(cot(x-a)+"tan"(x-b))/(cos(a-b))

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  11. Find the maximum and minimum values of the following expressions. (i)...

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  12. If sinA=3/5 and cosB=9/41, 0 < A < pi/2 and 0 < B < pi/2 then find the...

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  13. If cos A=4/(5), cosB=12/13 and (3pi)/2 < A, B < 2pi then find the valu...

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  14. Find the values of the following: t a n 15^0 ii. t a n 75^0

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  15. Find the values of the following: (i)tan105^0 ( ii.) tan((13pi)/12)

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  16. Evaluate the following: sin(7pi)/(12)cospi/4-cos(7pi)/(12)sinpi/4

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  17. Evaluate the following: cos(2pi/3)cos(pi/4)-sin(2pi/3)sin(pi/4)

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  18. Prove that: cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)="sin"(A+B)

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  19. Prove that: sin(n+1)A sin(n+2)A+cos(n+1)A cos(n+2)A=cos A

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  20. Prove that: cos(pi/4+x)+cos(pi/4-x\ )=sqrt(2)cosx

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