Is cos(2a)=(cot(a)-tan(a))/(csc(a)sec(a)) ?

The answer to whether cos(2a)=(cot(a)-tan(a))/(csc(a)sec(a)) is True

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prove cos(2a)=(cot(a)-tan(a))/(csc(a)sec(a))

prove

cos (2 a) = \frac{cot ( a ) - tan ( a )}{csc ( a ) sec ( a )}

True

Solution steps

cos (2 a) = \frac{cot ( a ) - tan ( a )}{csc ( a ) sec ( a )}

Manipulating right side

\frac{cot ( a ) - tan ( a )}{csc ( a ) sec ( a )}

Express with sin, cos

= cos^{2} (a) - sin^{2} (a)

Rewrite using trig identities

= cos (2 a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( θ )} = sin (θ) + cos (θ) cot (θ)

cos (a) cos (b) = \frac{1}{2} (cos (a - b) + cos (a + b))

sin^{2} (θ) (cot^{2} (θ) + 1) = 1

sin (a - b) = sin (a) cos (b) - cos (a) sin (b)

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

Is cos(2a)=(cot(a)-tan(a))/(csc(a)sec(a)) ?
The answer to whether cos(2a)=(cot(a)-tan(a))/(csc(a)sec(a)) is True