Question

razones trigonometricas de angulos multiples
simplifica la sgte expresion

E= (ctgx-tgx)* sen2x
alternativas
a) senx
b)cosx
c) 2senx
d) 2cos2x
e) -2cos2x

Answer 1

Usando el hecho de que
ctg x= 1/tgx
sen(2x) = 2 senx cosx
tgx = senx/cosx 
cos (2x) = cos²x-sen²x

E= sin(2x)(1/tgx - tgx) =  2 senx cosx ((1-tg²x)/tgx) = 2cos²x  (1- sen²x/cos²x)
= 2cos²x  (cos²x- sen²x)/cos²x = 2 Cos(2x)

R: d)

Answer 2

Recordemos:
• cotx = cosx / senx
• tanx = senx / cosx
• cos2x = cos²x - sen²x

PROCEDIMIENTO:


${(\cot x-tan x)\sin 2x=}\\\\\\{\left(\dfrac{\cos x}{\sin x}-\dfrac{\sin x}{\cos x}\right).2\sin x\cos x=}\\\\\\{\left(\dfrac{\cos ^2x-\sin^2x}{\sin x.\cos x}\right).2\sin x.\cos x=}\\\\\\{2(cos^2x-\sin^2x)=}\\\\\\{\boxed{2\cos 2x}}$


Salu2.!! :)
Wellington