Question

please solve this and please be quick ​

Answer 1

Answer:

Step-by-step explanation:

L.H.S:

=> 2/Cos²θ - 1/Cos⁴θ - 2/Sin²θ + 1/Sin⁴θ

//Take LCM of Cos items and SIn items seperately.

=> 2Cos²θ - 1 / Cos⁴θ + 1 - 2Sin²θ/Sin⁴θ

//We know that Cos2θ = 2Cos²θ - 1 = 1 - 2Sin²θ = Cos²θ - Sin²θ

=> Cos²θ - Sin²θ/Cos⁴θ   + Cos²θ - Sin²θ/Sin⁴θ

=> (Cos²θ - Sin²θ) (1/Cos⁴θ + 1/Sin⁴θ)

=> (Cos²θ - Sin²θ) (Sin⁴θ + Cos⁴θ)/ Sin⁴θCos⁴θ

=> (Cos²θ - Sin²θ)(Sin⁴θ + Cos⁴θ)/ Sin⁴θCos⁴θ

//We know that Cos²θ + Sin²θ = 1

=> (Cos²θ - Sin²θ)(Cos²θ + Sin²θ)(Sin⁴θ + Cos⁴θ) / Sin⁴θCos⁴θ

=> (Cos⁴θ + Sin⁴θ)( Cos⁴θ - Sin⁴θ)/Sin⁴θCos⁴θ

//We know that (a+b)(a-b) = a² - b²

=>(Cos⁴θ)² - (Sin⁴θ)² / Sin⁴θCos⁴θ

=> Cos⁴θ/Sin⁴θ - Sin⁴θ/Cos⁴θ

=> Cot⁴θ - Tan⁴θ

= R.H.S

Hence proved.

Answer 2

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