(sin a+tan a)(cos a+cot a)等于(1+sin a)(1+cos a) 证明恒等式成立
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(sin a+tan a)(cos a+cot a)等于(1+sin a)(1+cos a) 证明恒等式成立
(sin a+tan a)(cos a+cot a)
=(sin(a)+sin(a)/cos(a))/(cos(a)+cos(a)/sin(a)), 展开
=sin(a)*cos(a)+cos(a)+sin(a)+1)
合并成两个因式相乘的形式
=(sin(a)+1)(cos(a)+1) = 右式
=(sin(a)+sin(a)/cos(a))/(cos(a)+cos(a)/sin(a)), 展开
=sin(a)*cos(a)+cos(a)+sin(a)+1)
合并成两个因式相乘的形式
=(sin(a)+1)(cos(a)+1) = 右式
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