The discussion revolves around proving a trigonometric identity involving secant and cosecant functions. The original poster presents a fraction that combines these functions and seeks guidance on how to prove the identity.
Participants are actively engaging with the problem, providing guidance on how to manipulate the expressions. There is a recognition of confusion regarding the process of cross-multiplication, and some participants are clarifying their understanding of the method. Multiple interpretations of the steps are being explored.
There is an indication that participants are working under the constraints of homework rules, which may limit the extent of guidance provided. Some assumptions about the definitions and operations involved in trigonometric identities are being questioned.
I'm not sure what you mean by "cross multiply". To me, it means multiply both sides by the common denominator: here, that is (sin a cos a)(sin a+ cos a). You seem to have multiplied one side by (sin a+ cos a) and the other by (sin a cos a). Of course, that will not give you the same thing- you are multiplying the two sides by different things.VanKwisH said:hmmm i did cross multiply and then i got .....
((cosa*sina /cosa ) + ( cosa*sina /sina)) / sina+cosa for the left side
and then for the right side i got sina+cosa / cosa*sina for the right side ... is that right??
HallsofIvy said:I'm not sure what you mean by "cross multiply". To me, it means multiply both sides by the common denominator: here, that is (sin a cos a)(sin a+ cos a). You seem to have multiplied one side by (sin a+ cos a) and the other by (sin a cos a). Of course, that will not give you the same thing- you are multiplying the two sides by different things.