Is sin(a)sec(a)cot(a)=1 ?

The answer to whether sin(a)sec(a)cot(a)=1 is True

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prove sin(a)sec(a)cot(a)=1

prove

sin (a) sec (a) cot (a) = 1

True

Solution steps

sin (a) sec (a) cot (a) = 1

Manipulating left side

sin (a) sec (a) cot (a)

Express with sin, cos

cot (a) sec (a) sin (a)

Use the basic trigonometric identity:

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

= \frac{cos ( a )}{sin ( a )} sec (a) sin (a)

Use the basic trigonometric identity:

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

= \frac{cos ( a )}{sin ( a )} \cdot \frac{1}{cos ( a )} sin (a)

\frac{cos ( a )}{sin ( a )} \cdot \frac{1}{cos ( a )} sin (a) = 1

\frac{cos ( a )}{sin ( a )} \cdot \frac{1}{cos ( a )} sin (a)

Multiply fractions:

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

= \frac{cos ( a ) \cdot 1 \cdot sin ( a )}{sin ( a ) cos ( a )}

Cancel the common factor:

cos (a)

= \frac{1 \cdot sin ( a )}{sin ( a )}

Cancel the common factor:

sin (a)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

3 + 3 cos (x) = 2 (1 - cos^{2} (x))

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

\frac{cos ( 3 a ) cos ( 2 a )}{sin ( 3 a ) sin ( 2 a )} = \frac{cot ( 2 a )}{tan ( 3 a )}

\frac{1}{cos ^{2} ( θ )} = tan^{2} (θ) + 1

(sin (θ) - 1) (tan (θ) + sec (θ)) = - cos (θ)