Answer :
Let's solve the given trigonometric expression [tex]\(\operatorname{tg}(18^\circ) + \operatorname{tg}(27^\circ) + \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ)\)[/tex] step by step.
1. Calculate [tex]\(\operatorname{tg}(18^\circ)\)[/tex]:
The tangent of 18 degrees is approximately:
[tex]\[ \operatorname{tg}(18^\circ) \approx 0.3249196962329063 \][/tex]
2. Calculate [tex]\(\operatorname{tg}(27^\circ)\)[/tex]:
The tangent of 27 degrees is approximately:
[tex]\[ \operatorname{tg}(27^\circ) \approx 0.5095254494944288 \][/tex]
3. Calculate the product [tex]\(\operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ)\)[/tex]:
[tex]\[ \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ) \approx 0.3249196962329063 \times 0.5095254494944288 \approx 0.16501791490974126 \][/tex]
4. Add the results:
Now we need to add these three terms together:
[tex]\[ \operatorname{tg}(18^\circ) + \operatorname{tg}(27^\circ) + \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ) \approx 0.3249196962329063 + 0.5095254494944288 + 0.16501791490974126 \][/tex]
Combining these, we get:
[tex]\[ 0.3249196962329063 + 0.5095254494944288 + 0.16501791490974126 \approx 0.9999999999999999 \][/tex]
Hence, the final result for the given expression [tex]\(\operatorname{tg}(18^\circ) + \operatorname{tg}(27^\circ) + \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ)\)[/tex] is approximately:
[tex]\[ \boxed{1} \][/tex]
1. Calculate [tex]\(\operatorname{tg}(18^\circ)\)[/tex]:
The tangent of 18 degrees is approximately:
[tex]\[ \operatorname{tg}(18^\circ) \approx 0.3249196962329063 \][/tex]
2. Calculate [tex]\(\operatorname{tg}(27^\circ)\)[/tex]:
The tangent of 27 degrees is approximately:
[tex]\[ \operatorname{tg}(27^\circ) \approx 0.5095254494944288 \][/tex]
3. Calculate the product [tex]\(\operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ)\)[/tex]:
[tex]\[ \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ) \approx 0.3249196962329063 \times 0.5095254494944288 \approx 0.16501791490974126 \][/tex]
4. Add the results:
Now we need to add these three terms together:
[tex]\[ \operatorname{tg}(18^\circ) + \operatorname{tg}(27^\circ) + \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ) \approx 0.3249196962329063 + 0.5095254494944288 + 0.16501791490974126 \][/tex]
Combining these, we get:
[tex]\[ 0.3249196962329063 + 0.5095254494944288 + 0.16501791490974126 \approx 0.9999999999999999 \][/tex]
Hence, the final result for the given expression [tex]\(\operatorname{tg}(18^\circ) + \operatorname{tg}(27^\circ) + \operatorname{tg}(18^\circ) \times \operatorname{tg}(27^\circ)\)[/tex] is approximately:
[tex]\[ \boxed{1} \][/tex]
