Buktikan 2 sin kuadrat alfa = sin 2 alfa tan alfa
Matematika
annisakhrnii
Pertanyaan
Buktikan 2 sin kuadrat alfa = sin 2 alfa tan alfa
1 Jawaban
-
1. Jawaban maharani242
Tugas dan Jawaban Trigonometri (pembuktian identitas trigonometri)

UPLOADED BY
Schaum Mypha
TUGAS DAN JAWABAN TRIGONOMETRI (IDENTITAS TRIGONOMETRI)
Buktikan identitas berikut ini !1.
x (1 -
x) =
xJawab :
x (1 -
x) =
x
1
2
x
(
x) =
x
2
x
2
x
=
x
x =
x (TERBUKTI!)2.
cos
(sec x
–
cos x) =
xJawab :
cos
(sec x
–
cos x) =
xcos x (
1
–
cos x) =
xcos x
(
1−
) =
x
x =
x (TERBUKTI!)3.
sec x
–
cos x = sin x . tan xJawab : sec x
–
cos x = sin x . tan x
1
–
cos x = sin x . tan x
1−
2
x
=
sin x . tan x
2
x
=
sin x . tan xsin x .
in
=
sin x . tan xsin x . tan x = sin x . tan x (TERBUKTI!)
Ingat!1.
x +
x = 1
→
x = 1 -
x
2.
sec x =
1
Ingat!
tan x =
in


4.
cos b + sin b . tan b = sec bJawab : cos b + sin b . tan b = sec bcos b + sin b (
in
) = sec bcos b +
=
sec b
+
=
sec b
1
=
sec bsec b = sec b (TERBUKTI!)5.
−1
−1
=
4
bJawab :
−1
−1
=
4
b
−1
−1
=
4
b
=
4
b
1 −
x
1−
=
4
b
1 −
1−
x
=
4
b
x
b
=
4
b
b
x
b
=
4
b
4
b =
4
b (TERBUKTI!)6.
1 1+
+
1 1+
= 1
Jawab :
1 1+
+
1 1+
= 1
1 1+
+
11+(
)
= 1
1 1+
+
1
= 1
1 1+
+
1+
= 1
1+
1+
= 11 = 1
(TERBUKTI!)

7.
x +
x =
x .
xJawab :
x +
x =
x .
x
1
+
1
=
x .
x
+
.
=
x .
x
1
.
=
x .
x
1
x
1
=
x .
x (TERBUKTI!)8.
1−in
-
1+in
=
2 tan xJawab :
1−in
-
1+in
=
2 tan x
(1+in)−(1−in)(1−in)(1+in)
=
2 tan x
+in−+in1−
=
2 tan x
in
=
2 tan x
2 .
in
.
=
2 tan x2 tan x = 2 tan x (TERBUKTI!)
9.
1e−1
+
1e +1
=
2
cot .csc
Jawab :
1e−1
+
1e +1
=
2
cot .csc
1
−1
+
1
+1
=
2 cot a . csc a
1
+
1
∓
=
2
cot .csc
1−
+
1+
=
2
cot .csc
(1+)+ (1−)(1−)(1+)
=
2
cot .csc