verify the identity

1/sin(ø-1) + 1/sin(ø+1) = -2tanøsecø

Question

verify the identity 

1/sin(ø-1) + 1/sin(ø+1) = -2tanøsecø

calculusfunctions · Answer

Work with the left side.

Step 1: Add the fractions

anonymous · Answer

im confused how to even start it. like will the left side be 2sinø by adding them?

anonymous · Answer

i mean 2/sinø

calculusfunctions · Answer

How do you add fractions @biochems2k ? You first find the least common denominator, correct?

anonymous · Answer

correct, so multiply both of them by sinø - 1

calculusfunctions · Answer

$$Prove: \frac{ 1 }{ \sin Φ-1 }+\frac{ 1 }{ \sin Φ+1 }=2\tan Φ\sec Φ$$$$L.S.=\frac{ 1 }{ \sin Φ-1 }+\frac{ 1 }{ \sin Φ+1 }$$Least common denominator is  (sin Φ - 1)(sin Φ + 1).

Understand @biochems2k ?

calculusfunctions · Answer

Thus what is the sum of the two fractions?

calculusfunctions · Answer

If you don't know and would like me to show you the first step, please do not be embarrassed to say so.

anonymous · Answer

sorry, i was doing the work as you explained. after doing all that i at the end 2/sin^2ø - 1. am i correct?

anonymous · Answer

@calculusfunctions

anonymous · Answer

@calculusfunctions im actually stuck now. my answer didnt look correct

anonymous · Answer

@calculusfunctions after doing my math again i got 2sinø/sinø-1