Пошаговое объяснение:
ctg²x - tg²x = 4cos2x; 1/tg²x - tg²x = 4cos2x; ( (1 - tg²x) (1 + tg²x)) : tg²x = 4cos2x; ((1 - tg²x) · cos²x) : (cos²x · sin²x) = 4cos2x; (1 - sin²x/cos²x) : sin²x = 4cos2x; (cos²x - sin²x) : (cos²x · sin²x) = 4cos2x; ( 4cos2x) :(4cos²x · sin²x) = 4cos2x; cos2x (1/sin²x - 1) = 0; ОДЗ: sinx ≠ 0; cosx ≠ 0 ⇒cos2x = 0; 2x = π/2 + πn, n ∈ Z; X = π/4 + π/2n, n∈Z; ⇒ 1/ sin²2x = 1; sin²2x = 1 ⇒ sin2x = 1, sin2x = - 1; ⇒ 2x = π/2 + πn, n ∈ Z ; x = π/4 + π/2, n ∈ Z ответ: x = π/4 + π/2, n ∈ Z
1) 3/10+8,51+4/25 = 0,3+8,51+8/100 = 8,81+0,8 = 8,89
2) 9,65+5 1/4+1,7 = 11,35+5,25 = 16,6
3) 7 21/100+16,29+3/20 = 7,21+16,29+15/100 = 23,5+0,15 = 23,65
4) 6,02+16 1/2+12/25 = 6,02+16,5+48/100 = 22,52+0,48 = 23
5) 18,35+3 1/5+2,45 = 20,8+3 2/10 = 20,8+3,2 = 24
6) 27 7/50+2,36+4 1/2 = 27 14/100+2,36+4,5 = 27,14+6,86 = 34
7) 1 3/20+6,17+0,68 = 1 15/100+6,85 = 1,15+6,85 = 8
8) 2 2/25+0,6+3 7/20 = 2 8/100+0,6+3 35/100 = 2,08+0,6+3,35 = 2,68+3,35 = 6,03
9) 6 3/8+9,125+0,54 = 6 375/1000+9,665 = 6,375+9,665 = 16,04
Пошаговое объяснение:
ctg²x - tg²x = 4cos2x; 1/tg²x - tg²x = 4cos2x; ( (1 - tg²x) (1 + tg²x)) : tg²x = 4cos2x; ((1 - tg²x) · cos²x) : (cos²x · sin²x) = 4cos2x; (1 - sin²x/cos²x) : sin²x = 4cos2x; (cos²x - sin²x) : (cos²x · sin²x) = 4cos2x; ( 4cos2x) :(4cos²x · sin²x) = 4cos2x; cos2x (1/sin²x - 1) = 0; ОДЗ: sinx ≠ 0; cosx ≠ 0 ⇒cos2x = 0; 2x = π/2 + πn, n ∈ Z; X = π/4 + π/2n, n∈Z; ⇒ 1/ sin²2x = 1; sin²2x = 1 ⇒ sin2x = 1, sin2x = - 1; ⇒ 2x = π/2 + πn, n ∈ Z ; x = π/4 + π/2, n ∈ Z ответ: x = π/4 + π/2, n ∈ Z
1) 3/10+8,51+4/25 = 0,3+8,51+8/100 = 8,81+0,8 = 8,89
2) 9,65+5 1/4+1,7 = 11,35+5,25 = 16,6
3) 7 21/100+16,29+3/20 = 7,21+16,29+15/100 = 23,5+0,15 = 23,65
4) 6,02+16 1/2+12/25 = 6,02+16,5+48/100 = 22,52+0,48 = 23
5) 18,35+3 1/5+2,45 = 20,8+3 2/10 = 20,8+3,2 = 24
6) 27 7/50+2,36+4 1/2 = 27 14/100+2,36+4,5 = 27,14+6,86 = 34
7) 1 3/20+6,17+0,68 = 1 15/100+6,85 = 1,15+6,85 = 8
8) 2 2/25+0,6+3 7/20 = 2 8/100+0,6+3 35/100 = 2,08+0,6+3,35 = 2,68+3,35 = 6,03
9) 6 3/8+9,125+0,54 = 6 375/1000+9,665 = 6,375+9,665 = 16,04