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Question
The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.
Options
`sqrt(12)`
`1/sqrt(3)`
`sqrt(3)`
`sqrt(3)/2`
MCQ
Fill in the Blanks
Solution
The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is `underlinebb(sqrt(3))`.
Explanation:
∵ tan 60° = tan (40° + 20°)
`\implies sqrt(3) = (tan 40^circ + tan 20^circ)/(1 - tan 40^circ tan 20^circ)`
`\implies sqrt(3) - sqrt(3) tan 40^circ tan 20^circ` = tan 40° + tan 20°
∴ `tan 40^circ + tan 20^circ + sqrt(3) tan 40^circ tan 20^circ = sqrt(3)`
shaalaa.com
Trigonometric Functions of Sum and Difference of Angles
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