Math, asked by norulesmar, 9 months ago

4/sin^2theta-4/tan^2theta is equal

Answers

Answered by rishu6845

Answer:

Step-by-step explanation:

To find --> Value of

( 4 / Sin²θ - 4 / tan²θ )

Solution---> We know that

1 + Cot²θ = Cosec²θ

=> 1 = Cosec²θ - Cot²θ

=> Cosec²θ - Cot²θ = 1

Now

4 / Sin²θ - 4 / tan²θ

We know that,

1 / Sinθ = Cosecθ and 1 / tanθ = Cotθ

using this we get

= 4 ( 1 / Sin²θ ) - 4 ( 1 / tan²θ )

= 4 ( Cosec²θ ) - 4 ( Cot²θ )

= 4 ( Cosec²θ - Cot²θ )

Putting ( Cosec²θ - Cot²θ ) = 1

= 4 ( 1 )

= 4

Additional information--->

1) Sin²θ + Cos²θ = 1

Cos²θ = 1 - Sin²θ

Sin²θ = 1 - Cos²θ

2) 1 + tan²θ = Sec²θ

tan²θ = Sec²θ - 1

Sec²θ - tan²θ = 1

Answered by Aɾꜱɦ

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