SOLUTION: Simplifying trig identities. 2tanx sinx + 2cosx-cscx Please show steps

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Question 749617: Simplifying trig identities.
2tanx sinx + 2cosx-cscx
Please show steps

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Given, shown in abbreviated form: 2tan*sin+2cos-csc

2(sin/cos*)sin+2*cos-1/sin
2(sin/cos)*sin*(sin/sin)+2*cos*(cos/cos)*(sin/sin)-(1/sin)*(cos/cos)
(2sin^3+2(cos^2)sin-cos)/(sin*cos)
(2sin*(sin^2+cos^2)-cos)/(sin*cos)
Notice the identity expression sin^2+cos^2=1;
2sin*(1-cos)/(sin*cos)
.
2/cos-2cos/cos
highlight%282sec-2%29 or highlight%282%28sec-1%29%29

For some unknown reason, rendering was not working, so I removed the triple brackets tags on most of the steps. I know this makes reading more difficult.