Question

prove that cosec^4x-cosec^2x=cot^4x+cot^2x​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Given $cosec^4x-cosec^2x=cot^4x+cot^2x$

We need to prove that: LHS=RHS

Let us consider the left hand side is:

$cosec^4\Theta - cosec^2\Theta$

We can further write is as $cosec^4\Theta = (cosec^2\Theta )^2$.

Therefore,

$(cosec^2\Theta )2 - cosec^2\Theta$

We all know that, $cosec^2\Theta = 1+cot^2\Theta$

Putting the value in the above equation

$(1+cot^2\Theta)^2 - (1+cot^2\Theta )$

We can write $(1+cot^2\Theta )^2 = 1+cot^4\Theta + 2cot^2\Theta$,

Putting it in the equation as well:

$1+ cot^4\Theta + 2cot^2\Theta - 1 - cot^2 \Theta$

$= cot^4\Theta + cot^2\Theta$

According to the Equation,

RHS$= cot^4\Theta + cot^2\Theta$

LHS=RHS

Hence Proved

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