Is sin(A)sec(A)=tan(A) ?

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

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prove sin(A)sec(A)=tan(A)

prove

sin (A) sec (A) = tan (A)

True

Solution steps

sin (A) sec (A) = tan (A)

Manipulating left side

sin (A) sec (A)

Express with sin, cos

sec (A) sin (A)

Use the basic trigonometric identity:

sec (A) = \frac{1}{cos ( A )}

= \frac{1}{cos ( A )} sin (A)

Simplify

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

\frac{1}{cos ( A )} sin (A)

Multiply fractions:

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

= \frac{1 sin ( A )}{cos ( A )}

Multiply:

1 \cdot sin (A) = sin (A)

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

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

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

Use the basic trigonometric identity:

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

= tan (A)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) tan (x) cos (x) = 1

tan^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2}) - 5 = 3 tan (\frac{x}{2})

\frac{sin ( x )}{cos ^{2} ( x )} = tan (x) sec (x)

\frac{cot ( x ) + 2}{csc ( x )} = 2 sin (x) + cos (x)

(sec (x)) (sin (x)) = tan (x)