Question

give me corrrect answer​

Answer 1

If 2sinx - cos²x=1, then :

2(cos⁴x-cos²x) = -1.

Given that,

2sinx - cos²x = 1

We should find the value of

=> 2(cos⁴x - cos²x)

Before solving the question,

=> 2sinx= 1+cos²x

We know that,

1+cos²x=2cos²x

=> 2sinx - 2cos²x

Simplifying the terms,

=> Sinx = Cos²x

Now, consider the expression

=> 2(cos⁴x - Cos²x)

Cos⁴x can be written as ( Cos²x)²

So,

2[ ( Cos²x)² - Cos²x) ]

From the results,

Cos²x = Sinx.

Substituting the above value in the above expression,

=> 2(Sinx)² - Sinx).

=> 2(Sin²x - Sinx).

Simplifying the terms

=> 2 sin²n - 2sinx.

The above expression cannot be simplified further. Because the value of above expression are not given in the question.

Therefore,

The value of 2( Cos⁴x - Cos²x) = 2sin²x - 2sinx.

I hope it's will help you.

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