Question

if tanA +cotA =2 find the value of cosA​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

⇒ $cosA =\frac{1}\sqrt{2}}$

Step-by-step explanation:

Given :

tan A + cot A = 2,

Then, cos A = ?

Solution :

We know that,

$cot A=\frac{1}{tan A}$

So,

tan A + cot A = 2,

⇒ $tan A + \frac{1}{tan A} = 2$

⇒ $\frac{tan^2A+1}{tanA} = 2$

⇒ $tan^2A + 1 = 2 tanA$

⇒ $tan^2A - 2 tanA+1=0$

⇒ $tan^2A - tan A - tan A+1 = 0$

⇒ $tanA(tanA-1)-1(tanA-1)=0$

⇒ $(tanA-1)^2=0$

Taking square root both the sides,.

⇒ $tanA-1=0$

⇒ $tanA = 1$

⇒ $tanA=tan45$°

So,

⇒ $A=45$°

Hence,

$cosA=cos45$° $=\frac{1}\sqrt{2}}$

⇒ $cosA =\frac{1}\sqrt{2}}$