Question

sinA+ cosA=√3 then show that tanA+cotA=1​

Answer 1

Answer:

$\sin(a) + \cos(a) = \sqrt{3} \\ taking \: squaring \: on \: both \: sides \\ {( \sin(a) + \cos(a)) }^{2} = { \sqrt{(3)} }^{2} \\ { \sin(a) }^{2} + { \cos(a) }^{2} + 2 \sin(a \cos(a) ) = 3 \\ 1 + 2 \sin(a) \cos(a) = 3 \\ 2 \sin(a) \cos(a) = 3 - 1 \\ 2 \sin(a) \cos(a) = 2 \\ \sin(a) \cos(a) = 1$

$lhs \\ \tan(a) + \cot(a) \\ = \frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) } \\ = \frac{ { \sin(a) }^{2} + \cos(a) }{ \sin(a) \cos(a) } \\ = \frac{1}{ \cos(a) \sin(a) } \\ \frac{1}{1} = 1 \\ = rhs$

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