use fundamental identities find an equivalent expression involving only sines and cos

**nando29** · December 15th 2010, 01:25 AM

(Sec[θ] Csc[θ])/(Tan[θ] Cot[θ])

i believe the ans is (1)/(sin theta cos theta). however, can someone show each step because i'm getting lost in the division part. thankyou

**Prove It** · December 15th 2010, 01:29 AM

$\displaystyle \frac{\sec{\theta}\csc{\theta}}{\tan{\theta}\cot{\ theta}} = \frac{\frac{1}{\cos{\theta}}\,\frac{1}{\sin{\theta }}}{\frac{\sin{\theta}}{\cos{\theta}}\,\frac{\cos{ \theta}}{\sin{\theta}}}$

$\displaystyle = \frac{\frac{1}{\sin{\theta}\cos{\theta}}}{1}$

$\displaystyle = \frac{1}{\sin{\theta}\cos{\theta}}$ .

**nando29** · December 15th 2010, 01:40 AM

thank you very much

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