How do you simplify # 1/(cscx - cotx) + 1/(cscx + cotx)#?

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Answer 1 · 2015-08-30T01:10:34

#2cscx#

Rewrite in terms of #sinx# and #cosx#

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

#1/((1-cosx)/sinx)+1/((1+cosx)/sinx)#

#sinx/(1-cosx)+sinx/(1+cosx)#

#(sinx(1+cosx)+sinx(1-cosx))/((1-cosx)(1+cosx))#

#(sinx+sinxcosx+sinx-sinxcosx)/(1-cos^2x)#

#(sinx+sinx)/sin^2x#

#(2sinx)/sin^2x#

#2/sinx#

#2cscx#