Question

If sinx + cosx = $\frac{1}{5}$ then cot x is equal to ________.

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B)

The correct options are
A

B

sinx + cosx = $\frac{1}{5}$

We need to find the value of cotx.

If we square both sides of the given equation, we get,

$si{n}^{2}x+co{s}^{2}x+2sinx.cosx=\frac{1}{25}$

sin 2x = $\frac{1}{25}-1=\frac{-24}{25}$

sin2x can be written in terms of tanx.

$\frac{2tanx}{1+ta{n}^{2}x}=\frac{-24}{25}$
$\Rightarrow$ 12tan^x +25tanx + 12= 0
$\Rightarrow$ (3tanx+4)(4tanx+3)=0
$\Rightarrow$ tanx=$\frac{-4}{3}$ or$\frac{-3}{4}$