Jawaban:

Susut-sudut pada trigonometri, yaitu :

sin 0° = 0, cos 0° = 1, tan 0° = 0.

sin 30° = 1/2, cos 30° = 1/2 √3, tan 30° = 1/3 √3.

sin 45° = 1/2 √2, cos 45° = 1/2 √2, tan 45° = 1.

sin 60° = 1/2 √3, cos 60° = 1/2, tan 60° = √3.

sin 90° = 1, cos 90° = 0, tan 90° = ∞.

Mari kita lihat soal tersebut.

\begin{gathered}\frac{sin 45^o . sin 60^o + cos 45^o . cos 30^o}{tan 30^o . tan 60^o} \\= \frac{ \frac{1}{2} \sqrt{2}. \frac{1}{2} \sqrt{3}+ \frac{1}{2} \sqrt{2}. \frac{1}{2} \sqrt{3}} { \frac{1}{3} \sqrt{3}. \sqrt{3}} \\= \frac{ \frac{1}{4} \sqrt{6}+ \frac{1}{4} \sqrt{6}} { \frac{1}{3}.3} \\= \frac{ \frac{2}{4} \sqrt{6} } {1}\\= \frac{1}{2} \sqrt{6} \end{gathered}

tan30

o

.tan60

o

sin45

o

.sin60

o

+cos45

o

.cos30

o

=

3

1

3

.

3

2

1

2

.

2

1

3

+

2

1

2

.

2

1

3

=

3

1

.3

4

1

6

+

4

1

6

=

1

4

2

6

=

2

1

6