2sin²x + cos²x = 5sinxcosx
2sin²x - 5sinxcosx + cos²x = 0
2tg²x - 5tgx + 1 = 0
Пусть t = tgx.
2t² - 5t + 1 = 0
D = 25 - 2*4 = 25 - 8 = 17
t₁ = (5 + √17)/4
t₂ = (5 - √17)/4
Обратная замена:
tgx = (5 + √17)/4
x = arctg((5 + √17)/4) + πn, n ∈ Z.
tgx = (5 - √17)/4
x = ((5 - √17)/4) + πn, n ∈ Z
Х: 13/5=3 2/7 : 2 22/35
х*5/13=23/7 : 92/35
х*5/13=23/7 * 35/92
х*5/13=23/1 * 5/92
х*5/13= 115/92
х*5=115*13 : 92
5х=16,25
х=3,25
........... ...............
314,09 - 100%
x - 1%
x=1% × 314,09: 100%=3,1409
<span>f′(x)=<span><span>(<span><span>sin<span>(x)</span>+cos<span>(x)/</span></span><span>sin<span>(x)</span>−cos<span>(x)</span></span></span>)</span>′</span>=</span><span><span>=<span><span><span><span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span>′</span>⋅<span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>−<span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span>⋅<span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>′/</span></span><span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)^</span>2</span></span></span>=</span><span>=<span><span><span><span>(<span><span><span>(<span>sin<span>(x)</span></span>)</span>′</span>+<span><span>(<span>cos<span>(x)</span></span>)</span>′</span></span>)</span>⋅<span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>−<span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span></span><span>⋅<span>(<span><span><span>(<span>sin<span>(x)</span></span>)</span>′</span>−<span><span>(<span>cos<span>(x)</span></span>)</span>′</span></span>)/</span></span></span><span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)^</span>2</span></span>=</span><span>=<span><span><span><span>(<span>cos<span>(x)</span>+<span>(<span>−sin<span>(x)</span></span>)</span></span>)</span>⋅<span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>−<span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span></span><span>⋅<span>(<span>cos<span>(x)</span>−<span>(<span>−sin<span>(x)</span></span>)</span></span>)/</span></span></span><span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)^</span><span>2</span></span></span></span>