Question

If sinA+cosA=√2cosA find the value of cotA

Answer 1

sinA+cosA=√2cosA
dividing both sides by sinA,we have
1+cotA=√2cotA
{√2-1}cotA=1
cotA=1/{√2-1}

Answer 2

Answer:

The value is $\cot A=\sqrt2+1$

Step-by-step explanation:

Given : Expression $\sin A+\cos A=\sqrt2 \cos A$

To find : The value of cot A?

Solution :

$\sin A+\cos A=\sqrt2 \cos A$

Divide both side by sin A,

$\frac{\sin A}{\sin A}+\frac{\cos A}{\sin A}=\frac{\sqrt2 \cos A}{\sin A}$

$1+\cot A=\sqrt2 \cot A$

$\sqrt2 \cot A-\cot A=1$

$\cot A(\sqrt2 -1)=1$

$\cot A=\frac{1}{\sqrt2-1}$

$\cot A=\frac{1}{\sqrt2-1}\times \frac{\sqrt2+1}{\sqrt2+1}$

$\cot A=\frac{\sqrt2+1}{(\sqrt2)^2-1^2}$

$\cot A=\frac{\sqrt2+1}{2-1}$

$\cot A=\sqrt2+1$

Therefore, The value is $\cot A=\sqrt2+1$