Is (sin^2(x)+cos^2(x))^5=1 ?

The answer to whether (sin^2(x)+cos^2(x))^5=1 is True

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prove (sin^2(x)+cos^2(x))^5=1

prove

(sin^{2} (x) + cos^{2} (x))^{5} = 1

True

Solution steps

(sin^{2} (x) + cos^{2} (x))^{5} = 1

Manipulating left side

(sin^{2} (x) + cos^{2} (x))^{5}

Rewrite using trig identities

(sin^{2} (x) + cos^{2} (x))^{5}

Use the Pythagorean identity:

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

= 1^{5}

Apply rule

1^{a} = 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{cot ^{2} ( x ) - 1}{2 cot ( x )} = cot (2 x)

p ro v e csc (θ) = \frac{sec ( θ )}{tan ( θ )}

p ro v e \frac{cos ( 2 x ) + 1}{sin ( 2 x )} = cot (x)

p ro v e - tan (t) - \frac{cos ( t )}{sin ( t ) - 1} = sec (x)

p ro v e \frac{cot ( x )}{tan ( x ) sec ( x )} = csc (x) - 1

Is (sin^2(x)+cos^2(x))^5=1 ?
The answer to whether (sin^2(x)+cos^2(x))^5=1 is True