Question

find x (0<x<π/2) satisfying : (cos x/cosec+1) + (cos x/cosec-1) =2​

Answer 1

Answer:

π / 4 radians or 45°

Step-by-step explanation:

( cos x / cosec x + 1 ) + ( cos x / cosec x - 1 ) = 2

$\Rightarrow \sf \dfrac{cosx(cosecx - 1) + cosx(cosecx + 1)}{cosec^{2}x - 1} = 2$

$\Rightarrow \sf \dfrac{cosx.cosecx - cosx + cosx.cosecx + cosx}{cot^{2}x } = 2$

⇒ 2cosx.cosec x / cot²x = 2

⇒ cosx.cosec x / cot² x = 1

⇒ [ cos x × ( 1 / sin x ) ] / cot² x = 1

⇒ ( cos x / sin x ) / cot² x = 1

⇒ cot x / cot² x = 1

⇒ 1 / cot x = 1

⇒ tan x = 1

⇒ tan x = tan 45°

⇒ x = 45°

We know that

1° = π / 180 radians

⇒ x = 45° × ( π / 180 )

⇒ x = π / 4

Therefore the value of x is π / 4 radians or 45°.