Is (sec^2(a)-1)/(sec^2(a))=sin^2(a) ?

The answer to whether (sec^2(a)-1)/(sec^2(a))=sin^2(a) is True

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prove (sec^2(a)-1)/(sec^2(a))=sin^2(a)

prove

\frac{sec ^{2} ( a ) - 1}{sec ^{2} ( a )} = sin^{2} (a)

True

Solution steps

\frac{sec ^{2} ( a ) - 1}{sec ^{2} ( a )} = sin^{2} (a)

Manipulating left side

\frac{sec ^{2} ( a ) - 1}{sec ^{2} ( a )}

Express with sin, cos

= 1 - cos^{2} (a)

Rewrite using trig identities

= sin^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sec ( x )} = sec (x) - tan (x) \cdot sin (x)

2 sin^{2} (x) - sin (x) - 1 = 0

2 cos^{2} (θ) - 1 = cos (2 θ)

cos (3 B) = cos (B) (cos^{2} (B) - 3 sin^{2} (B))

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

Is (sec^2(a)-1)/(sec^2(a))=sin^2(a) ?
The answer to whether (sec^2(a)-1)/(sec^2(a))=sin^2(a) is True