Mathematics: If tanA+cotA=2 then find the value of cosA

AWH THANKS Step-by-step explanation:...

If tanA+cotA=2 then find the value of cosA - id27354297, imhorribleatmath90

onepunchman20

01.02.2022

cos A=

$\frac{1}{ \sqrt{2} }$

Step-by-step explanation:

We know,

cotA=

$\frac{1}{ \tan(a) }$

Substituting the value of cot A in the given equation, we get

$\tan( a) + \frac{1}{ \tan(a) } = 2$

$\frac{{ \tan }^{2} a + 1}{ \: \tan(a) } = 2$

${ \tan }^{2 \: } a \: + 1 = 2 tan \: a$

${ \tan }^{2} a - 2 \tan \: a + 1 = 0$

$( \tan \: a - 1) {}^{2 } = 0$

$\tan \: a - 1 = \sqrt{0}$

$\tan \: a = 1$

$\tan \: a \: = \tan \: 45$

a = 45

$\cos \: a = \cos \: 45$

$\cos \: a = \frac{1}{ \sqrt{2} }$

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