Question

$\cot(x) + \tan(x) = 2 \csc(x)$
​

Answer 1

Step-by-step explanation:

cotx + tanx = cosx/sinx + sinx/cosx

= (cos^2x + sin^2x)/sinx × cosx = 1/sinx × cosx =

(1×2)/sinx × cosx × 2 = 2/ sin2x = 2cosecx

Answer 2

$\huge{\underline{\bf\red{Questi {\mathbb{O}} n} :}}$

• Find the value of x .

$\huge{\underline{\: \bf\green{Answ {\mathbb{E}} r}\ \: :}}$

• The value of x is $\blue{\underline{\bf\green{\quad 60 \degree \quad}}}$

$\Large{\underline{\bf\purple{Giv {\mathbb{E}} n}\ :}}$

• $\boxed{ \cot(x) + \tan(x) = 2 \cosec(x) }$

$\Large{\underline{\bf\purple{To \ Fi {\mathbb{N}} d}\ :}}$

• Value of x .

$\huge{\underline{\bf\blue{Soluti {\mathbb{O}} n}\ :}}$

we have,

$\begin{aligned} \red{ \cot(x) + \tan(x) }& = \red{ 2 \cosec(x)} \\ \\ { \purple{ \implies}} \ \ \frac{ \cos(x) }{ \sin(x) } + \frac{\sin(x) }{ \cos(x) } & = \frac{2}{ \sin(x) } \\ \\ { \purple{ \implies}} \frac{ { \cos }^{2}(x) + { \sin }^{2}(x) }{ \cancel{\sin(x)} \cos(x) } & = \frac{2}{ \cancel{ \sin(x)}} \\ \\ { \purple{ \implies}} \qquad \qquad \ \ \: \frac{1}{ \cos(x) } & = 2 \\ \big[ \sf \because { \sin }^{2} \theta + { \cos }^{2} \theta = 1 \big] \\ \\ { \purple{ \implies}} \qquad \qquad \ \ \ \sec(x) & = 2\\ \\ { \purple{ \implies}} \qquad \qquad \ \ \ \sec(x) & = \sec(60 \degree)\\ \\ { \purple{ \implies}} \qquad \qquad \qquad \quad \green x & = \green{60 \degree} & & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$