Solve the following equations: 4 +2 +2 +1=0 - Vidyadip

Question

Solve the following equations:
$4\sin\text{x}\cos\text{x}+2\sin\text{x}+2\cos\text{x}+1=0$

✓

Answer

$4\sin\text{x}\cos\text{x}+2\sin\text{x}+2\cos\text{x}+1=0$
$\Rightarrow2\sin\text{x}(2\cos\text{x}+1)+1(2\cos\text{x}+1)=0$
$\Rightarrow(2\sin\text{x}+1)(2\cos\text{x+1})=0$
$\Rightarrow2\sin\text{x}+1=0$ or $2\cos\text{x}=-\frac{1}{2}$
$\Rightarrow\sin\text{x}=\sin\frac{7\pi}{6}$ or $\cos\text{x}=\frac{2\pi}{3}$
$\Rightarrow\text{x}=\text{n}\pi+(-1)^\text{n}\frac{7\pi}{6}$ or $\text{x}=2\text{n}\pi\pm\frac{2\pi}{3},\text{n}\in\text{Z}$

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 "5 Marks Questions" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Differentiate the following functions with respect to x:$\frac{\sin\text{x}-\text{x}\cos\text{x}}{\text{x}\sin\text{x}+\cos\text{x}}$

If are two different valus of X lying between 0 and which satisfy the equation $6\cos\text{x}+8\sin\text{x}=9$find the value of $\sin(\alpha+\beta).$

If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
fg

For any two sets A and B, prove that
$\text{(A}-\text{B)}\cup(\text{B}\cap\text{A})=\text{A}$

Find the equation of the ellips whose focus is (1, -2), the directrix $3\text{x}-2\text{y}+5=0$ and eccentricity equal to $\frac{1}{2}$

$\Bigg|\sin\text{x}\sin\Big(\frac{\pi}{3}-\text{x}\Big)\sin\Big(\frac{\pi}{3}+\text{x}\Big)\Bigg|\not<\frac{1}{4}$ for all values of x.

In each the following find the equation of the hyperbola satisfying the given conditions:
Foci $(0, \pm13), $ conjugate axis = 24

Prove that:
$\frac{\sin\text{A}\sin2\text{A}+\sin3\text{A}\sin6\text{A}}{\sin\text{A}\cos2\text{A}+\sin3\text{A}\cos6\text{A}}=\tan5\text{A}$

Find the point to which the origin should be shifted after a translation of axes so that the following equations will have no first deree terms:
$x^2 - 12x + 4 = 0$

Evaluate the following limits.
$\lim\limits_{\text{x} \rightarrow\pi}\frac{1-\sin\frac{\text{x}}{2}}{\cos\frac{\text{x}}{2}\Big(\cos\frac{\text{x}}{4}-\sin\frac{\text{x}}{4}\Big)}$