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

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

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prove ((-sin^2(a)+1))/(cos(a))=cos(a)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Cancel the common factor:

cos (a)

= cos (a)

= cos (a)

We showed that the two sides could take the same form

\Rightarrow True

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

sec (x) - tan (x) = cos (x)

tan (2 x) - tan (x) = \frac{tan ( x )}{cos ( 2 x )}

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

\frac{( sin ( a ) + sin ( 3 a ) )}{cos ( a ) + cos ( 3 a )} = tan (2 a)

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