Question

if x = 30 degree then 3 sin x - 4 sin ^3 x is​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• x = 30°.

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Value of 3 sinx - 4 sin³x

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

$\underline{\:\textsf{ Putting the value of x in the given equation :}}$

$\\ \\ \longrightarrow \displaystyle \sf \: 3 \sin30 ^ {\circ} - 4 \sin ^{3} 30 ^{ \circ}$

$\because\displaystyle \sf \: \sin30 ^ {\circ} = \dfrac{1}{2}$

$\longrightarrow \displaystyle \sf 3 \times \frac{1}{2} - 4 \times \bigg( \frac{1}{2} \bigg) ^{ 3}$

$\longrightarrow \displaystyle \sf \dfrac{3}{2} - 4 \times \dfrac{1}{8}$

$\longrightarrow \displaystyle \sf \dfrac{3}{2} - \dfrac{4}{8}$

$\longrightarrow \displaystyle \sf \frac{12 - 4}{8}$

$\longrightarrow \displaystyle \sf \cancel \dfrac{8}{8}$

$\longrightarrow \displaystyle \sf \underline{ \boxed{3 \sin30 ^ {\circ} - 4 \sin ^{3} 30 ^{ \circ} = 1}}$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\therefore\underline {\displaystyle \sf value \: of \: 3 \sin30 ^ {\circ} - 4 \sin ^{3} 30 ^{ \circ} \: is \: 1}$

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$\;\;\underline{\textbf{\textsf{ Know More :-}}}$

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$\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3} }{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }& 1 & \sqrt{3} & \rm Not \: De fined \\ \\ \rm cosec A & \rm Not \: De fined & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm Not \: De fined \\ \\ \rm cot A & \rm Not \: De fined & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}$

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Answer 2

Answer:

1 is your answer.........