(sinα+cosα)^2+(sinα-cosα)^2-cos^2α=tgαcosα•sinα

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вопрос

Let's simplify the left side of the equation first:

Expand (sinα+cosα)^2:
(sinα+cosα)^2 = sin^2α + 2sinαcosα + cos^2α

Expand (sinα-cosα)^2:
(sinα-cosα)^2 = sin^2α - 2sinαcosα + cos^2α

Add the two expanded terms together:
(sinα+cosα)^2 + (sinα-cosα)^2 = sin^2α + 2sinαcosα + cos^2α + sin^2α - 2sinαcosα + cos^2α
= 2sin^2α + 2cos^2α
= 2(sin^2α + cos^2α)
= 2

Substitute the simplified expression back into the original equation:
2 - cos^2α = tanαcosαsinα

Which simplifies further to:
2 = tanαcosαsinα + cos^2α