Is sin(θ)+(cos(θ))/(tan(θ))=csc(θ) ?

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

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prove sin(θ)+(cos(θ))/(tan(θ))=csc(θ)

prove

sin (θ) + \frac{cos ( θ )}{tan ( θ )} = csc (θ)

True

Solution steps

sin (θ) + \frac{cos ( θ )}{tan ( θ )} = csc (θ)

Manipulating left side

sin (θ) + \frac{cos ( 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

(1 + tan^{2} (u)) (1 - sin^{2} (u)) = 1

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

sin (x) = \frac{5}{13}

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

\frac{( 1 + cos ( 2 y ) )}{sin ^{2} ( y )} = 2 cot^{2} (y)

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