[HARD] Can You Help me With A Riddle of a Trig Question?

Question

Match each equation number with a equivalent letter, and then prove each one.
(1.): (csc (x) - sin (x))
(2.): (sin (x)/(sin (x)+ cos (x))
(3.): (2 sin 4(x)) (cos 4(x))
(4.): 1+ tan(x)tan(π/2)
(5.): ((sin (x)-1)/(sin (x) +1))

(A.): -(cos^2 (x)/(sin (x)+1)^2)
(B.): sec (x)
(C.): cos (x) cot (x)
(D.): sin 8(x)
(E.): tan/(1+ tan(x))

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Answer 1 · 2018-03-30T08:09:21

1 . #(csc (x) - sin (x))#
#=> 1/sinx - sinx#

#=> (1-sin^2x) /sinx#

#=> (cos^2x) /sinx#

#=>cos (x) cot (x)#

#color(white)(d#

2. #sin (x)/(sin (x)+ cos (x)#

#=>(sin x/cosx)/(sin x/cosx+ cos x/cosx#

#=>tan/(1+ tanx#

#color(white)(d#

3.: #(2 sin 4x) (cos 4x)#

#=>sin2(4x)#

#=>sin8x#

#color(white)(d#

5 .#((sin (x)-1)/(sin (x) +1))#

#=>((sin x-1)(sin x +1))/((sin x +1)(sin x +1))#

#=>((sin^2x-1)/(sin x +1)^2)#

#=>((-cos^2x)/(sin x +1)^2)#