Question #9394
Simplify:
sin(1+ ctg2x)
Solution
sin(1 + ctg2x)
cos2x
cos2x
sin1cos(
) cos1sin(
)
sin2x
sin2x
1
ctgx tgx
ctgx tgx
cos1sin (ctgx tgx) sin1cos(
) cos1sin(
)
2
2
2
2
2
ctgx
tgx
ctgx
tgx
ctgx
tgx
sin
sin
) cos1(sin
cos
cos
sin
)
2
2
2
2
2
2
ctgx
tgx
ctgx
tgx
ctgx
tgx
sin1sin
sin
cos1sin
cos
cos1cos
sin
2
2
2
2
2
2
tgx
ctgx
sin
cos(
1)
2
2
sin1cos(ctg2x)
1
sin1cos (ctgx tgx)
2
ctgx
tgx
sin1(cos
cos
2
2
ctgx
tgx
sin1cos
cos
2
2
tgx
ctgx
cos
sin(1
)
2
2
cos1sin(ctg2x)