Math, asked by cuteangel12, 1 year ago

solve the question in the given attachment .

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Answered by rishu6845

Answer:

Step-by-step explanation:

Given---> Cosecθ = x + 1 / 4x

To find---> Cosecθ + Cotθ = ?

Solution---> Given

Cosecθ = x + 1 / 4x

Squaring both sides we get

Cosec²θ = ( x + 1 / 4x )²

We have an identity

(a + b )² = a² + b² + 2ab , using it we get

=> 1 + Cot²θ = x² + (1 / 16x²) + 2 ( x ) ( 1 / 4x )

=> 1 + Cot²θ = x² + (1 / 16 x²) + ( 1 / 2 )

=> Cot²θ = x² + ( 1 / 16 x²) + ( 1 / 2 ) - 1

=> Cot²θ = x² + ( 1 / 16 x² ) - ( 1 / 2 )

= (x)² + ( 1 / 4x )² - 2 ( 1 / 4x ) ( x )

We have an identity

( a - b )² = a² + b² - 2ab , we get

=> Cot²θ = { x - ( 1 / 4x ) }²

Taking square root of both side

=> Cotθ = x - ( 1 / 4x )

Now ,

Cosecθ + Cotθ = x + ( 1 / 4x ) + x - ( 1 / 4x )

= x + x

Cosecθ + Cotθ = 2x

Answered by Aɾꜱɦ

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#answerwithquality #bal

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