Answer:
cos A=
[tex] \frac{1}{ \sqrt{2} } [/tex]
Step-by-step explanation:
We know,
cotA=
[tex] \frac{1}{ \tan(a) } [/tex]
Substituting the value of cot A in the given equation, we get
[tex] \tan( a) + \frac{1}{ \tan(a) } = 2[/tex]
[tex] \frac{{ \tan }^{2} a + 1}{ \: \tan(a) } = 2[/tex]
[tex] { \tan }^{2 \: } a \: + 1 = 2 tan \: a[/tex]
[tex] { \tan }^{2} a - 2 \tan \: a + 1 = 0[/tex]
[tex]( \tan \: a - 1) {}^{2 } = 0[/tex]
[tex] \tan \: a - 1 = \sqrt{0} [/tex]
[tex] \tan \: a = 1 [/tex]
[tex] \tan \: a \: = \tan \: 45[/tex]
[tex]a = 45[/tex]
[tex] \cos \: a = \cos \: 45[/tex]
[tex] \cos \: a = \frac{1}{ \sqrt{2} } [/tex]
