Is (1+sec(x))(1-cos(x))=sin(x)tan(x) ?

The answer to whether (1+sec(x))(1-cos(x))=sin(x)tan(x) is True

Popular >

prove (1+sec(x))(1-cos(x))=sin(x)tan(x)

prove

(1 + sec (x)) (1 - cos (x)) = sin (x) tan (x)

True

Solution steps

(1 + sec (x)) (1 - cos (x)) = sin (x) tan (x)

Manipulating left side

(1 + sec (x)) (1 - cos (x))

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

sin (x) tan (x)

We showed that the two sides could take the same form

\Rightarrow True

(sec (α)) (sec (α)) = tan (α)

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

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

(1 - cos (θ)) (1 + sec (θ)) = sec (θ) - cos (θ)

tan (x) csc (x) sec (x) = tan^{2} (x) + 1

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