Is (sin^2(x)+cos^2(x))^3=1 ?

The answer to whether (sin^2(x)+cos^2(x))^3=1 is True

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prove (sin^2(x)+cos^2(x))^3=1

prove

(sin^{2} (x) + cos^{2} (x))^{3} = 1

True

Solution steps

(sin^{2} (x) + cos^{2} (x))^{3} = 1

Manipulating left side

(sin^{2} (x) + cos^{2} (x))^{3}

Rewrite using trig identities

(sin^{2} (x) + cos^{2} (x))^{3}

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= 1^{3}

Apply rule

1^{a} = 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) + 1 = \frac{1}{cot ^{2} ( x )} + 1

sec (\frac{π}{4} + x) sec (\frac{π}{4} - x) = 2 sec (2 x)

cot (x) sec (x) (1 - cos^{2} (x)) = sin (x)

tan (x) + 2 = 2 + sec (x) sin (x)

2 sin^{3} (x) cos (x) + 2 sin (x) cos^{3} (x) = sin (2 x)

Is (sin^2(x)+cos^2(x))^3=1 ?
The answer to whether (sin^2(x)+cos^2(x))^3=1 is True