Question

The value of tan20+4sin20

Answer 1

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Answer 2

$\underline{\underline{\mathfrak{\Large{Solution : }}}}\\ \\ \\ \sf\implies\: tan20° + 4 sin20° \\ \\ \\ \sf\implies\dfrac{sin20°}{cos20°} + 4sin20° \\ \\ \\ \sf\implies\dfrac {sin20° + 4sin20°cos20°}{cos20°} \\ \\ \\ \sf\implies\dfrac {sin20° + 2sin (60° - 20°)}{cos20°}\\ \\ \\ \sf\implies\dfrac {sin20° + 2sin60°cos20° - 2cos60°sin20°}{cos20°}\\ \\ \\ \sf\implies\dfrac {sin20° + \sqrt {3} cos20° - sin20°}{cos20°}\\ \\ \\ \sf\implies\dfrac {\sqrt{3}cos20°}{cos20°}\\ \\ \\ \large{\implies{\boxed{\sf{\sqrt {3}}}}}$