Question

If sinx + cosx = $\frac{1}{5}$ then find the value of sinx.cosx.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We are given sinx + cosx = $\frac{1}{5}$ If we square both the sides we get

$si{n}^{2}x+co{s}^{2}x+2$ sinx.cosx on LHS.We can find sinx.cosx from this.

$(sinx+cosx{)}^2$ = $\frac{1}{25}$

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

1 + 2sinx.cosx = $\frac{1}{25}$

2 sinx.cosx = $\frac{1}{25}-1=\frac{-24}{25}$

sinx.cosx = $\frac{-12}{25}$