Question

verify the identity

Answer 1

\(\large\color{black}{ \displaystyle \frac{ \sec\theta }{\csc\theta-\cot\theta} -\frac{ \sec\theta }{\csc\theta+\cot\theta} }\)


\(\large\color{black}{ \displaystyle \frac{ \frac{1}{\cos \theta} }{\frac{1}{\sin \theta}-\frac{\cos \theta}{\sin \theta}} -\frac{ \frac{1}{\cos \theta} }{\frac{1}{\sin \theta} +\frac{\cos \theta}{\sin \theta}} }\)

Answer 2

\(\large\color{black}{ \displaystyle \frac{ \frac{1}{\cos \theta} }{\frac{1-\cos \theta}{\sin \theta}} -\frac{ \frac{1}{\cos \theta} }{\frac{1+\cos \theta}{\sin \theta}} }\)

\(\large\color{black}{ \displaystyle \frac{\sin \theta}{\cos \theta(1-\cos \theta)} - \frac{\sin \theta}{\cos \theta(1+\cos \theta)} }\)

Answer 3

\(\large\color{black}{ \displaystyle \frac{\sin \theta(1+\cos\theta)}{\cos \theta(1-\cos^2\theta)} - \frac{\sin \theta(1-\cos\theta)}{\cos \theta(1-\cos^2\theta)} }\)

\(\large\color{black}{ \displaystyle \frac{\sin \theta(1+\cos\theta)}{\cos \theta(\sin^2\theta)} - \frac{\sin \theta(1-\cos \theta)}{\cos \theta(\sin^2\theta)} }\)

\(\large\color{black}{ \displaystyle \frac{1+\cos\theta}{\cos \theta\sin\theta} - \frac{1-\cos \theta}{\cos \theta\sin\theta} }\)

Answer 4

\(\large\color{black}{ \displaystyle \frac{2\cos\theta}{\cos \theta\sin\theta} }\)

\(\large\color{black}{ \displaystyle 2\times \frac{1}{\sin\theta} }\)

Answer 5

and then....

Answer 6

i have no idea how to do this honestly

Answer 7

this si it. it is over
1/sine =cosecant

Answer 8

what does it mean by verify the identity though