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Find tan 20^(@) + tan40^(@) + sqrt(3)tan...

Find `tan 20^(@) + tan40^(@) + sqrt(3)tan20^(@)tan40^(@)`.

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The correct Answer is:
`sqrt(3)`
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Explore conceptually related problems

A =(cos 9^(@) - sin 9^(@))/(cos 9^(@) + sin 9^(@)) , B = (cos 21^(@) + sin 21^(@))/(cos21^(@) -sin21^(@)) and C= tan 20^(@) + tan40^(@) + sqrt(3)tan20^(@) tan40^(@) then descending order is:

A=(cos9^(@)-sin9^(@))/(cos9^(@)+sin 9^(@)), B=(cos21^(@)+sin21^(@))/(cos21^(@)-sin21^(@)) and C=tan 20^(@)+tan 40^(@)+sqrt(3)tan20^(@)tan40^(@) then descending order is

tan 70^(@) - tan 20^(@)=

Assertion (A): tan40^(@) + tan 80^(@) - sqrt(3)tan 40^(@) tan80^(@)=-sqrt(3) Reason ( R): tan( A + B) =tan A + tan B + tan(A + B) tan A tan B

Tan20^(@) + 2Tan50^(@) =

tan 20^(@) tan 40^(@) tan 60^(@) tan 80^@=

SRISIRI PUBLICATION-IPE SCANNER (TEXUAL BITS)-Very Short Questions (2 marks) (Trigonometric Ratios, Transformations)
  1. Simplify tan ((pi)/(4) +A) tan ((pi)/(4)-A)

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  2. Prove that tan 3A. tan2A.tanA = tan3A - tan 2A - tan A

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  3. Find tan 20^(@) + tan40^(@) + sqrt(3)tan20^(@)tan40^(@).

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  4. Prove that (sin theta + sin 2 theta )/(1+cos 0 + cos 2 theta )= tan th...

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  5. Express (1-costheta+sin theta)/(1+cos theta + sin theta) in terms of t...

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  6. Simplify (cot 55^(@)cot35^(@)-1)/(cot55^(@)+cot35^(@))

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  7. Express ((sqrt(3)cos 25^(@)+sin25^(@)))/(2) as a sine of an angle.

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  8. Expres sqrt3 sin 0 + cos 0 as a sine of an angle .

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  9. Express (cos theta - sin theta) as a cosine of an angle.

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  10. Express tan theta in terms of tan alpha, if sin (theta + alpha) = cos ...

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  11. Evaluate 6 sin 20^(@) - 8 sin^(3)20^(@).

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  12. Prove that (sin70^(@)-cos40^(@))/(cos50^(@)-sin20^(@)) = 1/(sqrt(3)).

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  13. Prove that sin 78^(@) + cos132^(@) = (sqrt(5)-1)/(4).

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  14. Prove that sin21^(@)cos9^(@)-cos84^(@)cos6^(@)=1/4.

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  15. Find the value of sin 34^(@) +cos 64^(@)- cos 4^(@)

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  16. Prove that sin50^(@)-sin70^(@)+sin10^(@)=0

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  17. Prove that 4(cos66^(@)+sin84^(@)) = sqrt(3) + sqrt(15).

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  18. Prove that cos 20^(@) cos 40^(@) - sin5^(@) sin 25^(@) = (sqrt(3)+1)/(...

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  19. Prove that cos theta + cos[(2pi)/3 + theta] + cos [(4pi)/(3) + theta] ...

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  20. Prove that cos A + cos((4pi)/3 -A) + cos ((4pi)/3 + A) = 0.

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