Is (tan(θ)cos(θ))/(sin(θ))=1 ?

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

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prove (tan(θ)cos(θ))/(sin(θ))=1

prove

\frac{tan ( θ ) cos ( θ )}{sin ( θ )} = 1

True

Solution steps

\frac{tan ( θ ) cos ( θ )}{sin ( θ )} = 1

Manipulating left side

\frac{tan ( θ ) cos ( θ )}{sin ( θ )}

Express with sin, cos

\frac{cos ( θ ) tan ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{cos ( θ ) \frac{s i n ( θ )}{c o s ( θ )}}{sin ( θ )}

\frac{cos ( θ ) \frac{s i n ( θ )}{c o s ( θ )}}{sin ( θ )} = 1

\frac{cos ( θ ) \frac{s i n ( θ )}{c o s ( θ )}}{sin ( θ )}

Multiply

cos (θ) \frac{sin ( θ )}{cos ( θ )} : sin (θ)

cos (θ) \frac{sin ( θ )}{cos ( θ )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ( θ ) cos ( θ )}{cos ( θ )}

Cancel the common factor:

cos (θ)

= sin (θ)

= \frac{sin ( θ )}{sin ( θ )}

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

sec (x) - cos (x) = sin (x) (tan (x))

sin (x) sin (3 x) = 4 sin (x) cos^{2} (x)

sec (\frac{π}{2} - t) = csc (t)

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

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