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Prove that: cotthetacot2theta+cot2thetac...

Prove that: `cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-cot3theta)`

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To prove the identity: \[ \cot \theta \cot 2\theta + \cot 2\theta \cot 3\theta + 2 = \cot \theta (\cot \theta - \cot 3\theta) \] we will follow these steps: ...
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  • TRIGONOMETRIC FUNCTIONS

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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. If t a nbeta=(nsinalphacosalpha)/(1-nsin^2alpha) , show that tan(alph...

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  2. If A+B=pi/4 , prove that: (1+t a n A)(1+t a n B)=2 (cotA-1)(cot...

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  3. Prove that: cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-c...

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  4. If tan(alpha+theta)=ntan(alpha-theta) , show that (n+1)sin2theta=(n-1...

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  5. Prove that: (sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(co...

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  6. If tan( pi cos theta) = cot ( pi sin theta) then sin (theta + pi/4) e...

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  7. Find the values of the following: (i)sin75^@ (ii) cos75^@ (iii) sin1...

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  8. If cotalpha=1/2,secbeta=-5/3,where piltalphalt(3pi)/2and pi/2 ltbetalt...

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  9. If sin A=3/5 ,0 < A < pi/2 and cosB=(-12)/(13),0 < B < (3pi)/2, find t...

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

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

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

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

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

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

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

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

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

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

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

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