Question

Can anyone prove this


4cosec2A ×cot 2A = cosec²A-sec²A

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Answer 1

Explanation:

`4cosec 2A * cot 2A=(4)/(sin 2A)*(cos 2A)/(sin 2A)\\\\=(4*(cos^(2)A-sin^(2)A))/(2sinA cosA*2sinAcosA)\\\\=(4*(cos^(2)A-sin^(2)A))/(4sin^(2)Acos^(2)A)\\\\=(cos^(2)A-sin^(2)A)/(sin^(2)Acos^(2)A)\\\\=\frac{cos^(2)A}{{sin^(2)Acos^(2)A}}-(sin^(2)A)/(sin^(2)Acos^(2)A)\\\\=(1)/(sin^(2)A)-(1)/(cos^(2)A)\\\\=cosec^(2)A-sec^(2)A`