Tanx/secx + cotx/cscx = sinx+cscx how do I verify this?

Question

#tanx/secx +cotx/cscx =sinx+cscx#

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Answer 1 · 2018-02-05T00:51:59

The question, as written, is not an identity. However, if the RH was meant to have #cosx# and not #cscx#, then we've proven it.

#tanx/secx+cotx/cscx=sinx+cscx#

I'm going to expand the LH side into terms of #sinx and cosx#:

#(sinx/cosx)/(1/cosx)+(cosx/sinx)/(1/sinx)=sinx+cscx#

#(sinx/cosx)(cosx)+(cosx/sinx)(sinx)=sinx+cscx#

#sinx+cosx=sinx+cscx#

And so the question, as written, is not an identity. However, if the RH was meant to have #cosx# and not #cscx#, then we've proven it.