Is cos^4(t)-sin^4(t)=1-2sin^2(t) ?

The answer to whether cos^4(t)-sin^4(t)=1-2sin^2(t) is True

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prove cos^4(t)-sin^4(t)=1-2sin^2(t)

prove

cos^{4} (t) - sin^{4} (t) = 1 - 2 sin^{2} (t)

True

Solution steps

cos^{4} (t) - sin^{4} (t) = 1 - 2 sin^{2} (t)

Manipulating left side

cos^{4} (t) - sin^{4} (t)

Factor

cos^{4} (t) - sin^{4} (t) : (cos^{2} (t) + sin^{2} (t)) (cos (t) + sin (t)) (cos (t) - sin (t))

= (cos (t) + sin (t)) (cos (t) - sin (t)) (cos^{2} (t) + sin^{2} (t))

Rewrite using trig identities

= 1 - 2 sin^{2} (t)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( x ) + csc ( x )}{1 + tan ( x )} = csc (x)

1 + tan^{2} (- θ) = sec^{2} (θ)

\frac{tan ( x ) + tan ( y )}{cot ( x ) + cot ( y )} = tan (x) tan (y)

\frac{cos ( \frac{π}{2} + x )}{cos ( π + x )} = tan (x)

cot (x) sec (x) = csc (x)

Is cos^4(t)-sin^4(t)=1-2sin^2(t) ?
The answer to whether cos^4(t)-sin^4(t)=1-2sin^2(t) is True