Prove cot^4 theta - cot^2 theta = 1

Answers 1

Explanation:

L.H.S=csc

4

θ−csc

2

θ

=(csc

2

θ)

2

−csc

2

θ

=(1+cot

2

θ)

2

−csc

2

θ {∵csc

2

θ=1+cot

2

θ}

=1+2cot

2

θ+cot

4

θ−csc

2

θ

=2cot

2

θ+cot

4

θ+1−csc

2

θ

=2cot

2

θ−cot

2

θ+cot

4

θ {∵1−csc

2

θ=−cot

2

θ}

=cot

2

θ+cot

4

θ=RHS proved.

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