Solve for x: 2 ^ -1 ( x) = ^ -1 (2cosec x) - Vidyadip

Question

$\text{Solve for x:}$
$2\tan^{-1}(\cos x) = \tan^{-1}(2\text{cosec x)} $

✓

Answer

$2\tan^{-1}(\cos\text{x}) = \tan^{-1}(2\text{cosec x)}$
$\Rightarrow\tan^{-1}\bigg(\frac{2 \cos \text{x}}{1 - \cos^{2}\text{x}}\bigg)= \tan^{-1}\bigg(\frac{2}{\sin \text{x}}\bigg)$
$\Rightarrow \sin\text{x}(\sin\text{x} - \cos \text{x}) = 0$
$\Rightarrow\sin\text{x} = \cos\text{x}$
the solution is $\text{x} = \frac{\pi}{4}$

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 "3 Marks Question" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Express $\overrightarrow{\text{AB}}$ in terms of unit vectors $\hat{\text{i}}\text{ and }\hat{\text{j}}$, when the point is:A(-6, 3), B(-2, -5)
Find $\Big|\overrightarrow{\text{AB}}\Big|$

Write a value of $\int\text{e}^{\text{x}}(\sin\text{x}+\cos\text{x})\text{dx}$

Find the point on the curve $y^2 = 8x$ for which the abscissa and ordinate change at the same rate.

For the principal values, evaluate the following:
$\tan^{-1}\big(\sqrt3\big)-\sec^{-1}(-2)$

Find the equation of a curve passing through the point $(0, 0)$ and whose differential equation is $y' = e^x$ sin x.

Evaluate the following intregals:
$\int\frac{1}{\sin^2\text{x}-\sin2\text{x}}\ \text{dx}$

Three relation $R_4$ is defined in set $A = \{a, b, c\}$ as follows:
$R_4 = \{(a, b), (b, c), (c, a)\}$
Find whether or not the relation $R_4$ on $A$ is:

Reflexive.
Symmetric.
Transitive.

Find the area of the parallelogram determinrd by the vectors:
$3\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$ and $\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$

Prove that the given vectors are coplanar:
$2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}},\ \hat{\text{i}}-3\hat{\text{j}}-5\hat{\text{k}}$ and $3\hat{\text{i}}-4\hat{\text{j}}-4\hat{\text{k}}$

Write the following in the simplest form:
$\sin^{-1}\Big\{\frac{\text{x}+\sqrt{1-\text{x}^2}}{\sqrt{2}}\Big\},-1<\text{x}<1$