Question

Cosec-1 x +sec-1 x=π2 1x1>1​

Answer 1

Step-by-step explanation:

can you please type your question properly

Answer 2

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Step By Step Solution :

Let f(x) = Cosec⁻¹ x +sec⁻¹ x = π/2 |x| > 1 --------- (1)

Differntiating with respect to x we get

f(x) = $\frac{d}{dx}$ ( Cosec⁻¹ x +sec⁻¹ x )

     = $\frac{d}{dx}$ ( sec⁻¹ x ) + $\frac{d}{dx}$  ( Cosec⁻¹ x )

     =  $\frac{1}{x\sqrt{x^{2} -1} } - \frac{1}{x\sqrt{x^{2} -1} }$

     =  0

Since f(x) = 0

f(x) is a constant function

Let f(x) = K

Let x = 2

Then f(2) = K

For any value of x f(x) =K  where |x| > 1 -----------(2)

From eqn 1

f(2) = Cosec⁻¹ 2 +sec⁻¹ 2

       = π/3 + π/6

       =  π/2

K =  π/2

f(x) = K =  π/2

Hence Proved

Cosec⁻¹ x +sec⁻¹ x = π/2

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It can also done through another method

But major method is given above

Here I'm givning 2nd method

But 1st is proper method

METHOD 2

= Cos (Cosec⁻¹ x +sec⁻¹ x )

= cos ( π/2 )

= cos ( 180 / 2 )

= cos 90°

= 0 which is less than 1

Hence proved

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