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Solve tanx+tan2x+tan3x=tanxtan2xtan3x ,x...

Solve `tanx+tan2x+tan3x=tanxtan2xtan3x ,x in [0,pi]`

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`tanx+tan2x+tan3x=tanx*tan2x*tan3x`
`tanx+tan2x=tanx*tan2x*tan3x-tan3x`
`tanx+tan2x=tan3x(tanx*tan2x-1)`
`(tanx+tan2x)/(tan3xtanx-1)=tan3x`
`(tanx(x+2x)=-tan3x`
`tan(x+2x)=-tan3x`
`tan3x=-tan3x`
`2tan3x=0`
...
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CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Solve (tan3x-tan2x)/(1+tan3xtan2x )=1

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  2. In a A B C ,ifA B=x , B C=x+1,/C=pi/3 , then the least integer value ...

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  3. Solve tanx+tan2x+tan3x=tanxtan2xtan3x ,x in [0,pi]

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  4. The value of cos(pi/7)+cos((2pi)/7)+cos((3pi)/7)+cos((4pi)/7)+cos((5pi...

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  5. In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley,...

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  6. A0, A1 ,A2, A3, A4, A5 be a regular hexagon inscribed in a circle of u...

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  7. General solution of tantheta+tan4theta+tan7theta=tanthetatan4thetatan7...

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  8. In triangleABC ,Delta=6, abc=60, r=1 Then the value of 1/a+1/b+1/c is ...

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  9. The total number of solution of the equation sin^4 x +cos^4 x = sin x ...

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  10. The numerical value of tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)+8tan((8pi...

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  11. In a triangle ABC , a =2,b=3 and sin A = (2)/(3) then cos C=

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  12. A right triangle has perimeter of length 7 and hypotenuse of length 3....

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  13. General solution of sin^2x-5sinxcosx-6cos^2x=0 is x=npi-pi/4,n in Z...

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  14. In triangle A B C , base B C and area of triangle are fixed. The loc...

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  15. A circle is drawn in a sector of a larger circle of radius r, as shown...

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  16. The sides of a triangle are three consecutive natural numbers and its ...

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  17. The sum of all the solution of the equation costhetacos(pi/3+theta)cos...

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  18. The least value of 2sin^2theta+3cos^2theta is 1 (b) 2 (c) 3 (d) ...

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  19. In triangle ABC, prove that the maximum value of tan(A/2)tan(B/2)tan(C...

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  20. Number of solution of the equation cos^4 2x+2sin^2 2x=17(cosx+sinx)^8,...

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