Is sec(θ)-tan(θ)sin(θ)= 1/(sec(θ)) ?

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

Popular >

prove sec(θ)-tan(θ)sin(θ)= 1/(sec(θ))

prove

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

True

Solution steps

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

Manipulating left side

sec (θ) - tan (θ) sin (θ)

Express with sin, cos

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

Rewrite using trig identities

= cos (θ)

Use the basic trigonometric identity:

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

= \frac{1}{sec ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

cot (- a) cos (- a) + sin (- a) = - csc (a)

sin (2 a) - tan (a) = tan (a) cos (2 a)

2 cos (x) tan (x) csc (x) = 2

sec^{2} (y) - cot^{2} (\frac{π}{2} - y) = 1

sin (\frac{π}{3} + x) - sin (\frac{π}{3} - x) = sin (x)

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