Question #8446f

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Answer 1 · 2018-02-24T08:49:21

#(4tan x-5 cos x)/(sec x+4 cot x)#

#=(sinxcosx(4sinx/cosx-5 cos x))/(sinxcosx(1/cos x+4 cos x/sinx))#

#=(4sin^2x-5 sinxcos^2 x)/(sinx+4 cos^2 x)#

#=(4sin^2x-5 sinx(1-sin^2 x))/(sinx+4 (1-sin^2 x))#

#=(4(4/5)^2-5 xx4/5(1-(4/5)^2 ))/(4/5+4 (1-(4/5)^2 )#

#=(64/25-36/25)/(4/5+36/25)#

#=(28/25)/(56/25)#

#=(28/25)xx(25/56)=1/2#