Is sec^2(x)+csc^2(x)=(csc(x)sec(x))^2 ?

The answer to whether sec^2(x)+csc^2(x)=(csc(x)sec(x))^2 is True

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prove sec^2(x)+csc^2(x)=(csc(x)sec(x))^2

prove

sec^{2} (x) + csc^{2} (x) = (csc (x) sec (x))^{2}

True

Solution steps

sec^{2} (x) + csc^{2} (x) = (csc (x) sec (x))^{2}

Manipulating left side

sec^{2} (x) + csc^{2} (x)

Express with sin, cos

= \frac{cos ^{2} ( x ) + sin ^{2} ( x )}{cos ^{2} ( x ) sin ^{2} ( x )}

Rewrite using trig identities

= \frac{1}{cos ^{2} ( x ) sin ^{2} ( x )}

Manipulating right side

(csc (x) sec (x))^{2}

Express with sin, cos

= \frac{1}{cos ^{2} ( x ) sin ^{2} ( x )}

We showed that the two sides could take the same form

\Rightarrow True

cot^{2} (x) = csc^{2} (x)

2 cot (θ) cot (2 θ) = cot^{2} (- 1)

\frac{cos ( x )}{sin ( x ) cot ^{2} ( x )} = tan (x)

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

\frac{( tan ^{2} ( x ) )}{sec ( x ) + 1} = \frac{( 1 - cos ( x ) )}{cos ( x )}

Is sec^2(x)+csc^2(x)=(csc(x)sec(x))^2 ?
The answer to whether sec^2(x)+csc^2(x)=(csc(x)sec(x))^2 is True