Question

Establish the following trig identity

Answer 1

\[\sin^4\theta - \cos^4\theta = 1 - 2\cos^2\theta\]

Answer 2

Equations:
\[\tan \theta = \frac{ \sin \theta }{ \cos \theta }\]
\[\cot \theta = \frac{ \cos \theta }{ \sin \theta }\]
\[\sec \theta = \frac{ 1 }{ \cos \theta}\]
\[\csc \theta = \frac{ 1 }{ \sin \theta}\]
\[\cot \theta = \frac{ 1 }{ \tan \theta}\]

Answer 3

\[\sin^2 \theta + \cos^2 \theta = 1\]

Answer 4

hint: \[A^2-B^2 = (A+B)(A-B)\]

Answer 5

and \[(sin^2(\theta))^2 = sin^4(\theta)\]

Answer 6

Thank you. I think I've got it.

\[= ( \sin^2 \theta + \cos^2 \theta ) (\sin^2 \theta - \cos^2 \theta)\]
Then just simplify to get sin^2 theta = 1 - cos^2 theta

Answer 7

yep. :)