Question

2. Prove cos 2x = cos4 x - sin" x​

Answer 1

Answer:

⭐ The proper Question : Prove cos 2x = cos4 x - sin4x

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$\tt \green{solution}$

cos 4 x−sin 4 x = (cos 2 x+sin 2 x)(cos 2 x−sin 2 x)=cos(2x)

From the Pythagorean identity

we know that,

cos 2 x+sin 2 x=1

so we can write

cos 2 x−sin 2 x=cos(2x)

Now,

cos(2x)=cos(x+x)

From the angle sum identity

we have,

cos(2x)=cos(x+x)=cos(x)cos(x)−sin(x)sin(x) cos(2x)

=cos(x+x)=cos 2 x−sin 2 x

Therefore ,

$cos 2x = cos4 x - sin4x$