Math, asked by Itnes14, 11 months ago

Cot4 - 1= cosec4 - 2cosec2

Answers

Answered by harendrachoubay
7

\cot^4 A- 1= \csc^4 A- 2\csc^2 A, proved.

Step-by-step explanation:

To prove that, \cot^4 A- 1= \csc^4 A- 2\csc^2 A.

L.H.S. = \cot^4 A- 1

= (\cot^2 A)- (1^2)^2

Using the algebraic identity,

a^{2}-b^{2}=(a+b)(a-b)

= [(\cot^2 A+ (1^2)][(\cot^2 A- (1^2)]

= (\cot^2 A+ 1)(\cot^2 A- 1)           ....(1)

Using the trigonometric identity,

\csc^2 A-\cot^2 A = 1

\csc^2 A=1+\cot^2 A

Equation (1) becomes

= (\csc^2 A)(\cot^2 A- 1)

= (\csc^2 A)(\csc^2 A-2)

= \csc^4 A- 2\csc^2 A

= R.H.S., proved.

Thus, \cot^4 A- 1= \csc^4 A- 2\csc^2 A, proved.

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