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

$$\begin{array}{rlcr}& 2cose{c}^2(30)+xsi{n}^2(60)-\frac{3}{4}ta{n}^2(30)=10& & \end{array}$$

Explanation:  

 Now simplify the equation below 

$$\begin{array}{rlcr}& 2cose{c}^2(30)+xsi{n}^2(60)-\frac{3}{4}ta{n}^2(30)=10& & \end{array}$$

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

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

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

$$OR8+\frac{3x}{4}-\frac{1}{4}=10$$

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

$$OR\frac{3x}{4}=\frac{1}{4}+2\Rightarrow \frac{9}{4}$$

$$OR\frac{3x}{4}=\frac{9}{4}$$

$$\Rightarrow 3x=9$$

$$\therefore x=3$$