If π&lt;α&lt;3π2 then the expression 4sin4α+sin22α+4cos2(π4−α2)

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If π&amp;lt;α&amp;lt;3π2 then the expression 4sin4α+sin22α+4cos2(π4−α2)

rakije2v · Accepted Answer

We note that in π&amp;lt;α&amp;lt;3π2, the value of sinα is negative.   Now,  4sin4α+sin22α   =4sin2α[sin2α+cos2α]   =|2sin⁡α|=−2sin⁡α   Now, you have correctly simplified the value of 4cos2(π4−α2) as 2+2sin⁡α   As a result, the answer must simply be 2

If π<α<3π2 then the expression 4sin4α+sin22α+4cos2(π4−α2)

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