Solution of the equation 2 tan -1cos x-tan -12 cosec x isA- x-2 n -4B- x-n -4C- x-n -2D- None of these

The correct option is B 2tan^ 1(cosx)=tan^ 1(2cosecx) ⇒ tan^ 1(2cosx/1 cos^2x)=tan^ 12 cosecx ⇒ 2cosx.cosec^2x=2cosecx cosecx(cotx 1)=0⇒ cotx=1 [∵ cosecx ≠ 0] ...

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Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

Solution of t...

Question

Solution of the equation $2 t a n^{- 1} (c o s x) = t a n^{- 1} (2 c o s e c x)$ is

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None of these

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Solution

The correct option is B

$2 t a n^{- 1} (c o s x) = t a n^{- 1} (2 c o s e c x)$
$\Rightarrow t a n^{- 1} (\frac{2 c o s x}{1 - c o s^{2} x}) = t a n^{- 1} 2 c o s e c x$
$\Rightarrow 2 c o s x . c o s e c^{2} x = 2 c o s e c x$
$c o s e c x (c o t x - 1) = 0 \Rightarrow c o t x = 1 [∵ c o s e c x \neq 0]$
$∴ x = n π + \frac{π}{4} n ϵ l$

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Similar questions

Solve the following equation for x:
$2 t a n^{- 1} (c o s x) = t a n^{- 1} (2 c o s e c x)$

2 t a n^{- 1} (cos x) = t a n^{- 1} (2 c o s e c x)

then

x = ?

Q. Solve for

x

2 {tan}^{- 1} (cos x) = {tan}^{- 1} (2 c o s e c x)

Q. If

2 {tan}^{- 1} (cos x) = {tan}^{- 1} (2 c o s e c x)

, then the value of x is.

Q. Solve the equation:

2 {tan}^{- 1} (cos x) = {tan}^{- 1} (2 c o s e c x)

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Solution of the equation 2tan−1(cosx)=tan−1(2cosecx) is

The correct option is B 2tan−1(cosx)=tan−1(2cosecx) ⇒tan−1(2cosx1−cos2x)=tan−12 cosecx ⇒2cosx.cosec2x=2cosecx cosecx(cotx−1)=0⇒cotx=1[∵cosecx≠0] ∴x=nπ+π4 n ϵ l

Solution of the equation $2 t a n^{- 1} (c o s x) = t a n^{- 1} (2 c o s e c x)$ is