Is cos(a)+sin(a)tan(a)=sec(a) ?

The answer to whether cos(a)+sin(a)tan(a)=sec(a) is True

Popular >

prove cos(a)+sin(a)tan(a)=sec(a)

prove

cos (a) + sin (a) tan (a) = sec (a)

True

Solution steps

cos (a) + sin (a) tan (a) = sec (a)

Manipulating left side

cos (a) + sin (a) tan (a)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( a )}

Rewrite using trig identities

sec (a)

We showed that the two sides could take the same form

\Rightarrow True

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

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

csc (2 x) = \frac{1}{2} sec (x) csc (x)

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

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

Is cos(a)+sin(a)tan(a)=sec(a) ?
The answer to whether cos(a)+sin(a)tan(a)=sec(a) is True