Question

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

Answer 1

cos A=

`(1)/( √(2) )`

Explanation:

We know,

cotA=

`(1)/( \tan(a) )`

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

`\tan( a) + (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 = √(0)`

`\tan \: a = 1`

`\tan \: a \: = \tan \: 45`

`a = 45`

`\cos \: a = \cos \: 45`

`\cos \: a = (1)/( √(2) )`