Question

if 3 cot theta equal to 4 then find sin theta + cos theta

Answer 1

I am using
$\alpha \: \: instead \: \: of \: theta$

$\cot( \alpha ) = \frac{4}{3}$
then

$\tan( \alpha ) = \frac{3}{4}$

$\sin( \alpha ) + \cos( \alpha )$

divided above eq by

$\cos( \alpha )$

we get

$\binom{ \sin( \alpha + \cos( \alpha ) }{ \cos( \alpha ) }$
$\binom{ \sin( \alpha ) } { \cos( \alpha ) } + \binom{ \cos( \alpha ) }{ \cos( \alpha ) }$

=>
$\tan( \alpha ) + 1$

=>
$\frac{3}{4} + 1$

=>
$\frac{7}{4}$

Answer 2

3 Cot theta = 4




Cot ¢ = 4/3 = B/P



Base = 4 , Perpendicular = 3 , H = ?



H² = B² + P²



H² = 4² + 3²




H² = 16 + 9


H = √25



H = 5


Therefore,

Cos ¢ = B/H = 4/5


And,


Sin ¢ = P / H = 3 / 5.


Therefore,


Sin ¢ + cos ¢ = 3/5 + 4/5 = 7/5.