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а) [latex]6cos^2t+5cost+1=0[/latex] [latex]cost=a, -1 \leq a \leq 1[/latex] [latex]6a^2+5a+1=0[/latex] [latex]D=5^2-4*6=1[/latex] [latex]a_{1} = \frac{-5-1}{2*6} = -\frac{1}{2} [/latex] [latex]a_{2} = \frac{-5+1}{2*6} = -\frac{1}{3} [/latex] [latex]cos t_{1} = - \frac{1}{2} [/latex] [latex] t_{1} =+- \frac{2 \pi }{3} +2 \pi k,[/latex] k ∈ Z [latex]cos t_{2} = - \frac{1}{3}[/latex] [latex] t_{2} = +- \pi -arccos \frac{1}{3} +2 \pi k,[/latex] k ∈ Z б) [latex]3+9cost=5sin^2t[/latex] [latex]3+9cost=5-5cos^2t[/latex] [latex]3+9cost-5+5cos^2t=0[/latex] [latex]5cos^2t+9cost-2=0[/latex] [latex]cost=x, -1 \leq x \leq 1[/latex] [latex]5x^2+9x-2=0[/latex] [latex]D=9^2-4*5*(-2)=121=11^2[/latex] [latex] x_{1} = \frac{-9-11}{2*5} =-2[/latex] [latex] x_{2} = \frac{-9+11}{2*5} = \frac{1}{5} [/latex] [latex] x_{1} =-2 \leq -1,[/latex] ⇒ не удовлетворяет условию [latex] cost_{2} = \frac{1}{5} [/latex] [latex] t_{2} =+- arccos \frac{1}{5} +2 \pi k,[/latex] k ∈ Z