Is 1/(sec(x))=sec(x)-tan(x)*sin(x) ?

The answer to whether 1/(sec(x))=sec(x)-tan(x)*sin(x) is True

Popular >

prove 1/(sec(x))=sec(x)-tan(x)*sin(x)

prove

\frac{1}{sec ( x )} = sec (x) - tan (x) \cdot sin (x)

True

Solution steps

\frac{1}{sec ( x )} = sec (x) - tan (x) sin (x)

Manipulating right side

sec (x) - tan (x) sin (x)

Express with sin, cos

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

Rewrite using trig identities

= cos (x)

Use the basic trigonometric identity:

cos (x) = \frac{1}{sec ( x )}

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

We showed that the two sides could take the same form

\Rightarrow True

2 sin^{2} (x) - sin (x) - 1 = 0

2 cos^{2} (θ) - 1 = cos (2 θ)

cos (3 B) = cos (B) (cos^{2} (B) - 3 sin^{2} (B))

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

sin (θ + \frac{π}{2}) = cos (θ)

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