Is sin(θ)tan(θ)=sec(θ)-cos(θ) ?

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

Popular >

prove sin(θ)tan(θ)=sec(θ)-cos(θ)

prove

sin (θ) tan (θ) = sec (θ) - cos (θ)

True

Solution steps

sin (θ) tan (θ) = sec (θ) - cos (θ)

Manipulating left side

sin (θ) tan (θ)

Express with sin, cos

= \frac{sin ^{2} ( θ )}{cos ( θ )}

Rewrite using trig identities

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

Manipulating right side

sec (θ) - cos (θ)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ( x ) + tan ( x )}{csc ( x )} = sec (x)

cot (θ) + 1 = csc (θ) (cos (θ) + sin (θ))

cos^{5} (x) = (1 - sin^{2} (x))^{2} cos (x)

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

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

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