Is cot^2(a)=cos^2(a)+(cot(a)cos(a))^2 ?

The answer to whether cot^2(a)=cos^2(a)+(cot(a)cos(a))^2 is True

Popular >

prove cot^2(a)=cos^2(a)+(cot(a)cos(a))^2

prove

cot^{2} (a) = cos^{2} (a) + (cot (a) cos (a))^{2}

True

Solution steps

cot^{2} (a) = cos^{2} (a) + (cot (a) cos (a))^{2}

Manipulating right side

cos^{2} (a) + (cot (a) cos (a))^{2}

Express with sin, cos

= \frac{cos ^{4} ( a ) + cos ^{2} ( a ) sin ^{2} ( a )}{sin ^{2} ( a )}

Factor

\frac{cos ^{4} ( a ) + cos ^{2} ( a ) sin ^{2} ( a )}{sin ^{2} ( a )} : \frac{cos ^{2} ( a ) ( cos ^{2} ( a ) + sin ^{2} ( a ) )}{sin ^{2} ( a )}

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

Rewrite using trig identities

= \frac{cos ^{2} ( a )}{sin ^{2} ( a )}

Rewrite using trig identities

cot^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ^{2} ( v )}{sin ( v )} = csc (v) - sin (v)

sin (2 x) = 2 cot (x) sin^{2} (x)

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

cos (x) sec (x) = 1

\frac{sec ( t ) - cos ( t )}{sec ( t )} = sin^{2} (t)

Is cot^2(a)=cos^2(a)+(cot(a)cos(a))^2 ?
The answer to whether cot^2(a)=cos^2(a)+(cot(a)cos(a))^2 is True