erity each identity tan x sin cos tanrsinx 10 sin x cos x c

erity each identity: tan x sin cos tanrsinx 10, sin x + cos x cot x = csc x 9. sec2x-1

Solution

9)tanxsinx/(sec²x -1)

we know sec²x -tan²x =1 is an identity =>sec²x -1 =tan²x

=tanxsinx/(tan²x)

=sinx/tanx

write tanx as sinx/cosx

=sinx/(sinx/cosx)

=sinxcosx/sinx

=cosx

therefore tanxsinx/(sec²x -1) =cosx

10)sinx +cosxcotx

write cotx as cosx/sinx

=sinx + cosx(cosx/sinx)

=(sinx*sinx +cosxcosx)/sinx

=(sin²x +cos²x)/sinx

weknow sin²x +cos²x =1 is an identity

=1/sinx

=cscx

sinx +cosxcotx =cscx