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

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

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prove (1-cos^2(a))(1+tan^2(a))=tan^2(a)

prove

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

True

Solution steps

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

Manipulating left side

(1 - cos^{2} (a)) (1 + tan^{2} (a))

Rewrite using trig identities

= (1 - cos^{2} (a)) sec^{2} (a)

Express with sin, cos

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

Rewrite using trig identities

= \frac{sin ^{2} ( a )}{cos ^{2} ( a )}

Rewrite using trig identities

tan^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( \frac{13}{5} )} = csc (\frac{13}{5})

tan (\frac{θ}{2}) = \frac{1 - cos ( θ )}{2}

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

\frac{cos ( x ) + sin ( x )}{sin ( x )} - cot (x) = 1

cot (x) sec (x) csc^{2} (x) - cot^{3} (x) sec (x) = csc (x)

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