Question

Tg 10 * tg80 + ctg 20 *ctg 70

Answer 1

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Answer 2

To calculate the value of the expression, we need to use trigonometric identities. Here's the step-by-step solution:

1. Convert degrees to radians:

   • 80 degrees = (80 * π) / 180 radians ≈ 1.3962634 radians
   • 20 degrees = (20 * π) / 180 radians ≈ 0.3490659 radians
   • 70 degrees = (70 * π) / 180 radians ≈ 1.2217305 radians

2. Apply trigonometric identities:

   • tg(x) = tan(x)
   • ctg(x) = 1 / tan(x)

3. Calculate the values:

   • tg(80 degrees) ≈ tan(1.3962634) ≈ 5.6712818
   • ctg(20 degrees) ≈ 1 / tan(0.3490659) ≈ 2.7474774
   • ctg(70 degrees) ≈ 1 / tan(1.2217305) ≈ 0.2732395

Now, plug the values into the original expression:

Tg(10) * tg(80) + ctg(20) * ctg(70) ≈ 10 * 5.6712818 + 2.7474774 * 0.2732395

Now, perform the calculations:

Tg(10) * tg(80) + ctg(20) * ctg(70) ≈ 56.712818 + 0.7500508

Finally, add the values:

Tg(10) * tg(80) + ctg(20) * ctg(70) ≈ 57.4628688

So, the value of the expression Tg(10) * tg(80) + ctg(20) * ctg(70) is approximately 57.46.