Is cos(θ)(cot(θ)+tan(θ))=csc(θ) ?

The answer to whether cos(θ)(cot(θ)+tan(θ))=csc(θ) is True

Popular >

prove cos(θ)(cot(θ)+tan(θ))=csc(θ)

prove

cos (θ) (cot (θ) + tan (θ)) = csc (θ)

True

Solution steps

cos (θ) (cot (θ) + tan (θ)) = csc (θ)

Manipulating left side

cos (θ) (cot (θ) + tan (θ))

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ( θ )}

Rewrite using trig identities

csc (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (- θ) = - sin (θ)

- sin (x) = sin (- x)

sec (θ) cot (θ) sin (θ) = 1

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

cos^{2} (2 x) - sin^{2} (2 x) = cos (4 x)

Is cos(θ)(cot(θ)+tan(θ))=csc(θ) ?
The answer to whether cos(θ)(cot(θ)+tan(θ))=csc(θ) is True