Question

If sin θ + cos θ = 2 , then evaluate : tan θ + cot θ

Answer 1

$\sin(x) + \cos(x) = 2$
${( \sin(x) + \cos(x) ) }^{2} = {2}^{2}$
${ \sin {}^{2} (x) } + \cos{}^{2}(x) + 2 \sin(x )\cos(x) ) = 4$
$1 + 2 \sin(x) \cos(x) = 4$
$2 \sin(x) \cos(x) = 3$
$\sin(x) \cos(x) = \frac{3}{2}$
Now,
$\tan(x) + \cot(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) }$
$= \frac{ { \sin }^{2}(x) + { \cos }^{2}(x) }{ \sin(x) \cos(x) }$
$= \frac{1}{ \frac{3}{2} }$
$= \frac{2}{3}$

Thank You :)<3

NOTE: $sin(x) + cos(x)$ can never be greater than $\sqrt(2)$

Answer 2

Answer:

2/3

but actually question is wrong as sina+ cosa can never be 2

sina + cosa =  1.414 is max possible value

Step-by-step explanation:

replaning thetha by a

sina + cosa = 2

squaring both sides

sin^2a + cos^2a + 2sinacosa = 4

2sinacosa = 3 (as sin^a + cos^2a =1)

sinacosa= 3/2

tana + cota

= sina/cosa + cosa/sina

= (sin^2a + cos^2a)/(cosasina)

= 1/3/2)

= 2/3