If ( sin x/ cos x) × ( sec x/ operatornamecosec x) × ( tan x/ cot x)=9, where x ∈(0, (π/2)), then the value of x is equal to

Question

If ( sin x/ cos x) × ( sec x/ operatornamecosec x) × ( tan x/ cot x)=9, where x ∈(0, (π/2)), then the value of x is equal to (A) (π/4) (B) (π/3) (C) (π/2) (D) π

Tardigrade Admin · Accepted Answer

( sin x/ cos x) × ( sec x/ operatornamecosec x) × ( tan x/ cot x)=9 ⇒ tan x × tan x × ( tan x/ cot x)=9 ⇒ tan 4 x=9 ⇒ tan x=± √3 ⇒ x=(π/3) as x ∈(0, (π/2))

Q. If $\frac{s i n x}{c o s x} \times \frac{s e c x}{cosec x} \times \frac{t a n x}{c o t x} = 9$ , where $x \in (0, \frac{π}{2})$ , then the value of $x$ is equal to

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{2}$

$π$

$\frac{s i n x}{c o s x} \times \frac{s e c x}{cosec x} \times \frac{t a n x}{c o t x} = 9$
$\Rightarrow tan x \times tan x \times \frac{t a n x}{c o t x} = 9 \Rightarrow tan^{4} x = 9$
$\Rightarrow tan x = \pm 3 \Rightarrow x = \frac{π}{3}$ as $x \in (0, \frac{π}{2})$

Q. If cosxsinx​×cosecxsecx​×cotxtanx​=9, where x∈(0,2π​), then the value of x is equal to

4π​

3π​

2π​

π

cosxsinx​×cosecxsecx​×cotxtanx​=9 ⇒tanx×tanx×cotxtanx​=9⇒tan4x=9 ⇒tanx=±3​⇒x=3π​ as x∈(0,2π​)

Q. If $\frac{s i n x}{c o s x} \times \frac{s e c x}{cosec x} \times \frac{t a n x}{c o t x} = 9$ , where $x \in (0, \frac{π}{2})$ , then the value of $x$ is equal to

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{2}$

$π$

$\frac{s i n x}{c o s x} \times \frac{s e c x}{cosec x} \times \frac{t a n x}{c o t x} = 9$
$\Rightarrow tan x \times tan x \times \frac{t a n x}{c o t x} = 9 \Rightarrow tan^{4} x = 9$
$\Rightarrow tan x = \pm 3 \Rightarrow x = \frac{π}{3}$ as $x \in (0, \frac{π}{2})$