Solve the following equation: 2 ^ 2 x-5 +2=0 - Vidyadip

Question

Solve the following equation:
$2\cos^{2}\text{x}-5\cos\text{x}+2=0$

✓

Answer

We have,
$2\cos^{2}\text{x}-5\cos\text{x}+2=0$
$\Rightarrow2\cos^{2}\text{x}-4\cos\text{x}-\cos\text{x}+2=0$ [Use factorization]
$\Rightarrow2\cos\text{x}(\cos\text{x}-2)-1(\cos\text{x}-2)=0$
$\Rightarrow(2\cos\text{x}-1)(\cos\text{x}-2)=0$
$\Rightarrow\text{Either}$
$2\cos\text{x}-1=0$ or $\cos\text{x}-2=0$
$\Rightarrow\cos\text{x}=\frac{1}{2}$ or $\cos\text{x}=2$
$\Rightarrow\cos\text{x}=\cos\frac{\pi}{3}$ $\big[$This is not possible as $-1<\cos\text{x}<1\big]$
$\Rightarrow\text{x}=2\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{z}$
Thus,
$\text{x}=2\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{z}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(4 Marks)" from Trigonometric Equations→Trigonometric Equations — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement

(a)vowels are always together.

(b)vowels are never together.

(c)O is at the beginning and end with T.

(d)starting with a vowel and ending with a consonant.

Find the trigonometric functions of : – 120°

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{(1+\text{x})^{{6}}-1}{(1+\text{x})^2-1}$

Find the equation of the straight lines passing through the following pair of points:
$(\text{a}\cos\alpha, \ \text{a} \ \sin\alpha)$ and $(\text{a}\cos\beta, \ \text{a} \ \sin\beta)$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow2}\bigg\{\frac{1}{\text{x}-2}-\frac{2(2\text{x}-3)}{\text{x}^2-3\text{x}^2+2\text{x}}\bigg\}$

Show that the line $3 x-4 y+10=0$ is a tangent to the hyperbola $x^2-4 y^2=20$. Also, findthe point of contact.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3\sin^2\text{x}-2\sin\text{x}^2}{3\text{x}^2}$

The line $2 x-y+6=0$ meets the circle $x^2+y^2+10 x+9=0$ at $A$ and $B$. Find the equation of circle with AB as diameter.

If $a, b, c$ are in G.P., prove that:
$(\text{a}+2\text{b}+2\text{c})(\text{a}-2\text{b}+2\text{c})=\text{a}^2+4\text{c}^2$

In any triangle $\mathrm{ABC}_r \sin \mathrm{A}-\cos \mathrm{B}=\cos \mathrm{C}$. Show that $\angle \mathrm{B}=\frac{\pi}{2}$.