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Evaluate the following: cos(2pi)/3cospi/...

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

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To evaluate the expression \( \cos\left(\frac{2\pi}{3}\right) \cos\left(\frac{\pi}{4}\right) - \sin\left(\frac{2\pi}{3}\right) \sin\left(\frac{\pi}{4}\right) \), we can use the cosine of a sum formula: ### Step-by-step Solution: 1. **Identify the formula**: We know from trigonometric identities that: \[ \cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b) \] ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. Find the values of the following: tan(13pi)/(12)

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

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

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

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

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

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

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

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

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  12. Prove that : sin^2 6x-sin^2 4x=s in2x\ s in\ 10 x

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  13. Prove that: cos^2 2x-cos^2 6x=s in4x s in8x

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  14. Prove that: (cos^2 33^@-cos^2 57^)/(sin(21)^@-cos(21))=-1/sqrt(2)

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

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

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  17. If s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  18. If s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  19. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  20. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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