4-2 tg^2135°+ctg^3 120°/3tg^245°-4sin ^2 150°+4cos^2 120°

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вопрос

First, let's simplify the given expression:

tg^2135° = tg^915° = tg^75°

ctg^3 120° = ctg 60° = 1/tg 60° = 1/sqrt(3)

3tg^245° = 3tg^65°

4sin^2 150° = 4(sqrt(3)/2)^2 = 43/4 = 3

4cos^2 120° = 4*(1/2)^2 = 4/4 = 1

Therefore, the simplified expression is:

tg^75° + 1/sqrt(3) / 3tg^65° - 3 + 1

Now we can calculate the numerical result:

tg^75° ≈ 2.7475
1/sqrt(3) ≈ 0.5774
tg^65° ≈ 2.1445

Substitute these values into the expression:

2.7475 + 0.5774 / 3*2.1445 - 3 + 1 ≈ 2.7475 + 0.5774 / 6.4335 - 3 + 1 ≈ 2.7475 + 0.5774 / 6.4335 - 3 + 1 ≈ 2.7475 + 0.0900 - 3 + 1 ≈ 0.8375

Therefore, the final answer is approximately 0.8375.