Solve the following equations: -1 - - Vidyadip

Question

Solve the following equations:
$\sin\text{x}\ \tan\text{x}-1\tan\text{x}-\sin\text{x}$

✓

Answer

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

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.(5 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

Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3x + y = 12 which is intercepted between the axes of coordinates.

Sum the following series to $n$ terms:
$1 + 4 + 13 + 40 + 121 + .....$

Discuss the continuity of $f(x)$ at $x=\frac{\pi}{4}$ where,
$f(x)=\frac{(\sin x+\cos x)^3-2 \sqrt{2}}{\sin 2 x-1}$, for $x \neq \frac{\pi}{4}$
$=\frac{3}{\sqrt{2}}$, for $x=\frac{\pi}{4}$

Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent.

$x^2+y^2+4 x-12 y+4=0$

$x^2+y^2-2 x-4 y+4=0$

Show that the product of the lengths of the perpendicular segments drawn from the foci

to any tangent line to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is equal to 16 .

By using Cramer's rule solve the following linear equations.
$x+y-z=1,8 x+3 y-6 z=1,-4 x-y+3 z=1$

Evaluate the following limits: $\lim _{x \rightarrow 0}\left[\frac{\cos (a x)-\cos (b x)}{\cos (c x)-1}\right]$

Table below shows the frequency $f$ with which $'x'$ alpha particles radiated from a diskette:

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
$f$	$51$	$203$	$383$	$525$	$532$	$408$	$273$	$139$	$43$	$27$	$10$	$4$	$2$

Calculate the mean and variance.

Find the angles between the following pairs of straight lines:
3x + 4y - 7 = 0 and 4x - 3y + 5 = 0

Let $\text{f}:[0,\infty)\rightarrow\text{R}$ and $\text{g}:\text{R}\rightarrow\text{R}$ be defined by $\text{f(x)}=\sqrt{\text{x}}$ and g(x) = x. Find f + g, g - g, fg and $\frac{\text{f}}{\text{g}}$