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If sin(picostheta)=cos(pi sintheta),t h ...

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

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To solve the problem where we have \( \sin(\pi \cos \theta) = \cos(\pi \sin \theta) \) and we need to find \( \sin 2\theta \), we can proceed with the following steps: ### Step 1: Rewrite the equation We start with the equation: \[ \sin(\pi \cos \theta) = \cos(\pi \sin \theta) \] Using the co-function identity, we can rewrite the cosine term: ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(ta...

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

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

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

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

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

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

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

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

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

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

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

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  13. Find the values of the following: tan(13pi)/(12)

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

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  15. Evaluate the following: cos(2pi)/3cospi/4-sin(2pi)/3sinpi/4

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

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

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  19. Prove that: cos((3pi)/4+x)-cos((3pi)/4-x\ )=sqrt(2)sinx

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

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