Question

Evaluate θ if:
(θ-10) = cot (20-40)​

Answer 1

Step-by-step explanation:

\sin(x) + \cos(x) = 2sin(x)+cos(x)=2

{( \sin(x) + \cos(x) ) }^{2} = {2}^{2}(sin(x)+cos(x))2=22

{ \sin {}^{2} (x) } + \cos{}^{2}(x) + 2 \sin(x )\cos(x) ) = 4sin2(x)+cos2(x)+2sin(x)cos(x))=4

1 + 2 \sin(x) \cos(x) = 41+2sin(x)cos(x)=4

2 \sin(x) \cos(x) = 32sin(x)cos(x)=3

\sin(x) \cos(x) = \frac{3}{2}sin(x)cos(x)=23

Now,

\tan(x) + \cot(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) }tan(x)+cot(x)=cos(x)sin(x)+sin(x)cos(x)

= \frac{ { \sin }^{2}(x) + { \cos }^{2}(x) }{ \sin(x) \cos(x) }=sin(x)cos(x)sin2(x)+cos2(x)

= \frac{1}{ \frac{3}{2} }=231

= \frac{2}{3}=32

Thank You :)<3

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