185/VB02. problem / Math - Solved Math Problems

MR-185 / 1353. problem

Prove the following identity::

$s i n^{4} α + c o s^{2} α + s i n^{2} α \cdot c o s^{2} α = 1$

s i n^{4} α + c o s^{2} α + s i n^{2} α \cdot c o s^{2} α

= s i n^{2} α (s i n^{2} α + c o s^{2} α) + c o s^{2} α

= s i n^{2} α \cdot 1 + c o s^{2} α

= s i n^{2} α + c o s^{2} α

= 1

$s i n^{4} α + c o s^{2} α + s i n^{2} α \cdot c o s^{2} α = 1$

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