Question

if A=30°, then proof
(1+2tanA.cosA÷sinA+cosA) + (1-sinA.cosA÷sinA-cosA)= 1​

Answer 1

$\frac{1 + 2 \times \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{2} }{ \frac{1}{2} + \frac{ \sqrt{3} }{2} } + \frac{1 - \frac{1}{2} \times \frac{ \sqrt{3} }{2} }{ \frac{1}{2} - \frac{ \sqrt{3} }{2} } \\ \\ = > \frac{2}{ \frac{1}{2} + \frac{ \sqrt{3} }{2} } + \frac{ \frac{4 - \sqrt{3} }{4} }{ \frac{1}{2} - \frac{ \sqrt{3} }{2} } \\ \\ = > \frac{4}{1 + \sqrt{3} } + \frac{2(4 - \sqrt{3}) }{4( 1 - \sqrt{3}) } \\ \\ = > \frac{4}{1 + \sqrt{3} } - \frac{4 - \sqrt{3} }{2( \sqrt{3} - 1 )} \\ \\ = > \frac{8 \sqrt{3} - 8 - (4 - \sqrt{3})(1 + \sqrt{3} )}{2(3- 1)} \\ \\ = > \frac{8 \sqrt{3} - 8 - (4 + 4 \sqrt{3} - \sqrt{3} - 3)}{4} \\ \\ = > \frac{8 \sqrt{3} - 8 - 3 \sqrt{3} - 1 }{4} \\ \\ = > \frac{5 \sqrt{3} - 7}{4}$

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