С. (1-tg^2t)cos^2t докажите тождества 1-sinα=2sin^2(45°-α/2) sin^2(3π/4+2t)=1-sin4t/2 p.s / знак дроби
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Ответы на вопрос:
(1-tg²t)·cos²t=cos²t-sin²tcos²t/cos²t=cos²t-sin²t=cos2t; 1-sinα=2sin²(45⁰-α/2); 2sin²(45-α/2)=2(sin45⁰·cosα/2-cos45⁰·sinα/2)²= =2·(√2/2·cosα/2-√2/2·sinα/2)²=2·2/4(cosα/2-sinα/2)²= =(cosα/2-sinα/2)²=cos²α/2-2cosα/2·sinα/2+sin²α/2=1-sinα; sin²(3π/4+2t)=1-sin4t/2; sin²(3π/4+2t)=(sin(3π/4)·cos2t+cos(3π/4)·sin2t)²= =(sin(π-π/4)·cos2t+cos(π-π/4)·sin2t)²= =(sinπ/4·cos2t+(-cosπ/4)·sin2t)²= =(√2/2cos2t-√2/2sin2t)²=2/4(cos²2t-2sin2t·cos2t+sin²2t)= =1/2(1-sin4t);
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