Is (cos(θ))/(1+sin(θ))+tan(θ)=sec(θ) ?

The answer to whether (cos(θ))/(1+sin(θ))+tan(θ)=sec(θ) is True

Popular >

prove (cos(θ))/(1+sin(θ))+tan(θ)=sec(θ)

prove

\frac{cos ( θ )}{1 + sin ( θ )} + tan (θ) = sec (θ)

True

Solution steps

\frac{cos ( θ )}{1 + sin ( θ )} + tan (θ) = sec (θ)

Manipulating left side

\frac{cos ( θ )}{1 + sin ( θ )} + tan (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( θ )}

Rewrite using trig identities

sec (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (x) \cdot tan (x) = sin (x)

\frac{sin ( 2 θ )}{sin ( θ )} - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

\frac{sec ( x )}{csc ( x )} + \frac{sin ( x )}{cos ( x )} = 2 tan (x)

\frac{sin ( θ ) + tan ( θ )}{1 + sec ( θ )} = sin (θ)

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

Is (cos(θ))/(1+sin(θ))+tan(θ)=sec(θ) ?
The answer to whether (cos(θ))/(1+sin(θ))+tan(θ)=sec(θ) is True