How can you simplify $sin^4a + cos^4a$ ?

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Answer 1 · 2017-07-17T15:15:02

$sin^4a + cos^4a = 1 - 2sin^2acos^2a = 1 - 1/2sin^2(2a)$ .

Note that

$(sin^2a + cos^2a)^2 = sin^4a + 2sin^2acos^2a + cos^4a$

We see that $sin^2x + cos^2x = 1$ , so that

$1 = sin^4a + 2sin^2acos^2a + cos^4a$

Therefore,

$sin^4a + cos^4a = 1 - 2sin^2acos^2a$

Hopefully this helps!

How can you simplify sin^4a + cos^4asin^4a + cos^4a?