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

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

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prove cos^4(a)-sin^4(a)+1=2cos^2(a)

prove

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

True

Solution steps

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

Manipulating left side

cos^{4} (a) - sin^{4} (a) + 1

Factor

1 - sin^{4} (a) : - (sin^{2} (a) + 1) (sin (a) + 1) (sin (a) - 1)

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

Rewrite using trig identities

= 2 cos^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

(csc (θ)) (sec (θ)) - cot (θ) = tan (θ)

(cos (x)) (cot (x)) = csc (x) - sin (x)

\frac{sec ( - x )}{tan ( x ) + cot ( x )} = sin (x)

sin (3 a) + sin (a) = 4 sin (a) - 4 sin^{3} (a)

sin (2 t) = 2 sin (t) (cos (t))

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