Question

if sin theta + cos theta is equal to 3 then find tan theta + cot theta​

Answer 1

Step-by-step explanation:

$\sin( \alpha ) + \cos( \alpha ) = 3 \\ \sin(a) = 3 - \cos(a) \\ \cos(a) = 3 - \sin(a) \\ \\ \tan(a) = \frac{ \sin(a) }{ \cos(a) } \\ \\ \tan(a) = \frac{3 - 3 + \sin(a) ) }{3 - \sin(a) } \\ \\ \tan(a) = \frac{ \sin(a) }{3 - \sin(a) } \\ \\ \cot(a) = \frac{1}{ \tan(a) } \\ \\ \cot(a) = \frac{3 - \sin(a) }{ \sin(a) } \\ \\ \\ \\ \tan(a) + \cot(a) = \frac{ \sin(a) }{3 - \sin(a) } + \frac{3 - \sin(a) }{ \sin(a) } \\ \\ = \frac{ { \sin(a) }^{2} + (3 - \sin(a)) }{3 \sin(a) - { \sin(a) }^{2} } \\ \\ = \frac{ \sin(a) }{ \sin(a) } \frac{ \sin(a) + 3 - 1 }{3 - \sin(a) } \\ \\ = \frac{ \sin(a) + 2 }{3 - \sin(a) }$

Answer 2

$\Large\frak{\underline{\underline{Answer:}}}$

$\sin( \alpha ) + \cos( \alpha ) = 3 \\ \sin(a) = 3 - \cos(a) \\ \cos(a) = 3 - \sin(a) \\ \\ \tan(a) = \frac{ \sin(a) }{ \cos(a) } \\ \\ \tan(a) = \frac{3 - 3 + \sin(a) ) }{3 - \sin(a) } \\ \\ \tan(a) = \frac{ \sin(a) }{3 - \sin(a) } \\ \\ \cot(a) = \frac{1}{ \tan(a) } \\ \\ \cot(a) = \frac{3 - \sin(a) }{ \sin(a) } \\ \\ \\ \\ \tan(a) + \cot(a) = \frac{ \sin(a) }{3 - \sin(a) } + \frac{3 - \sin(a) }{ \sin(a) } \\ \\ = \frac{ { \sin(a) }^{2} + (3 - \sin(a)) }{3 \sin(a) - { \sin(a) }^{2} } \\ \\ = \frac{ \sin(a) }{ \sin(a) } \frac{ \sin(a) + 3 - 1 }{3 - \sin(a) } \\ \\ = \frac{ \sin(a) + 2 }{3 - \sin(a) }$