1+sina/cosa如何化简成cot(π/4-a/2)
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1+sina/cosa如何化简成cot(π/4-a/2)
一步步来
一步步来
1+sina/cosa=(sin²a/2+cos²a/2+2sina/2cosa/2)/(cos²a/2-sin²a/2)
=(sina/2+cosa/2)²/[(cosa/2+sina/2)(cosa/2-sina/2)]
=(sina/2+cosa/2)/(cosa/2-sina/2)
=[√2(√2/2sina/2+√2/2cosa/2)]/[√2(√2/2cosa/2-√2/2sina/2)]
=(sina/2cosπ/4+sinπ/4cosa/2)]/(cosπ/4cosa/2-sinπ/4sina/2)
=sin(a/2+π/4)/cos(π/4+a/2)
=tan(a/2+π/4)
=cot[π/2-(a/2+π/4)]
=cot(π/4-a/2)
=(sina/2+cosa/2)²/[(cosa/2+sina/2)(cosa/2-sina/2)]
=(sina/2+cosa/2)/(cosa/2-sina/2)
=[√2(√2/2sina/2+√2/2cosa/2)]/[√2(√2/2cosa/2-√2/2sina/2)]
=(sina/2cosπ/4+sinπ/4cosa/2)]/(cosπ/4cosa/2-sinπ/4sina/2)
=sin(a/2+π/4)/cos(π/4+a/2)
=tan(a/2+π/4)
=cot[π/2-(a/2+π/4)]
=cot(π/4-a/2)
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