Class X Session 2023-24 Question 25

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 25

Find the value of x if

\begin{flalign} & 2\;cosec^2(30) + xsin^2(60)-\frac{3}{4}tan^2(30)= 10 &\ \end{flalign}

Explanation:  

 Now simplify the equation below 

\begin{flalign} & 2\;cosec^2(30) + xsin^2(60)-\frac{3}{4}tan^2(30)= 10 &\\ \end{flalign}

\[ \Rightarrow 2\times(2)^2+ x\left(\frac{\sqrt{3}}{2}\right)^2 -\frac{3}{4}\left(\frac{1}{\sqrt{3}}\right)^2 = 10 \]

we know that value of cosec(30) , sin(60)and tan(30) putting their values

\[ \Rightarrow 2\times 4 + x\frac{3}{4} - (\frac{3}{4}\times\frac{1}{3} )= 10 \]

\[ OR \; 8 + \frac{3x}{4} - \frac{1}{4} = 10 \]

\[ OR \; \frac{3x}{4} = \frac{1}{4} +(10-8) \]

\[ OR \; \frac{3x}{4} = \frac{1}{4} +2 \Rightarrow \frac{9}{4} \]

\[ OR \; \frac{3x}{4} = \frac{9}{4} \]

\[\Rightarrow {3x} = {9} \]

\[\therefore{x} = {3} \]