Question

Find the value of x for which

(i) 2cosec 30° + x sin?60° - - tan²30º = 10
4​

Answer 1

Answer:

x = 3

Step-by-step explanation:

Correct Question :-

Find the value of x for which :-

$2csc^230^{\circ}+xsin^260^{\circ}-\dfrac{3}{4}tan^230^{\circ}=10$

Solution :-

$2(2)^2+x\left(\dfrac{\sqrt{3}}{2}\right)^2-\dfrac{3}{4}\left(\dfrac{1}{\sqrt{3}}\right)^2=10$

$2\times 4 + x\times \dfrac{3}{4}-\dfrac{3}{4}\times \dfrac{1}{3}=10$

$8+\dfrac{3x}{4}-\dfrac{1}{4}=10$

$\dfrac{32+3x-1}{4}=10$

$\dfrac{31+3x}{4}=10$

31 + 3x = 40

3x = 40 - 31

3x = 9

x = 9/3

x = 3

Know More :-

$\sf\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$