Question

2sinx-cos2x=1 then
2(cos^4x-cos^2x)=-1​

Answer 1

Given:

Given that, $2sinx-cos2x=1$.

To find:

We should find the value of $2(cos^4x-cos^2x)$.

Solution:

Before solving the question, first we need to expand the given expression.

According to the question,

$\Rightarrow 2sinx-cos2x=1$

Rearranging the above terms,

$\Rightarrow 2sinx=1+cos2x$

We know that, $1+cos2x=2cos^2x$.

$\Rightarrow 2sinx=2cos^2x$

Simplifying the terms,

$\Rightarrow sinx=cos^2x$

Now, consider the expression

$\Rightarrow 2(cos^4x-cos^2x)$

$cos^4x$ can be written as $(cos^2x)^2$.

So,

$\Rightarrow 2((cos^2x)^2-cos^2x)$

From the above result, $cos^2x= sinx$.

Substituting the above value in the above expression,

$\Rightarrow 2((sinx)^2-sinx)$

$\Rightarrow 2(sin^2x-sinx)$

Simplifying the terms,

$\Rightarrow 2sin^2x-2sinx$

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

Therefore, the value of $2(cos^4x-cos^2x)=2sin^2x-2sinx$.