[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))

1327 views around the world

You can reuse this answer
Creative Commons License

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 . $((sin (x)-1)/(sin (x) +1))$

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

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

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