Is sin(θ)sec(θ)=tan(θ) ?

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

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prove sin(θ)sec(θ)=tan(θ)

prove

sin (θ) sec (θ) = tan (θ)

True

Solution steps

sin (θ) sec (θ) = tan (θ)

Manipulating left side

sin (θ) sec (θ)

Express with sin, cos

sec (θ) sin (θ)

Use the basic trigonometric identity:

sec (θ) = \frac{1}{cos ( θ )}

= \frac{1}{cos ( θ )} sin (θ)

Simplify

\frac{1}{cos ( θ )} sin (θ) : \frac{sin ( θ )}{cos ( θ )}

\frac{1}{cos ( θ )} sin (θ)

Multiply fractions:

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

= \frac{1 sin ( θ )}{cos ( θ )}

Multiply:

1 \cdot sin (θ) = sin (θ)

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

\frac{sin ( θ )}{cos ( θ )} = tan (θ)

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) - sin (x) = cos (x) cot (x)

cos^{2} (θ) (1 + tan^{2} (θ)) = 1

\frac{cot ^{2} ( x )}{csc ( x )} = csc (x) - sin (x)

tanh (x) = \frac{sinh ( x )}{cosh ( x )}

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