Question

If the value of sinA is $\frac{4}{5},$ then what will be the value of ${\sin }^{2}A+co{s}^{2}A?$

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. 1
• D. $\frac{3}{5}$

Answer 1

The correct option is C 1

Given: $\sin A=\frac{4}{5}=\frac{4k}{5k}$ (Let)

Now, perpendicular = 4k and hypotenuse = 5k.

So, base$=\sqrt{(5k{)}^2-(4k{)}^2}=\sqrt{25k^2-16k^2}$

$\Rightarrow \text{base}=\sqrt{9k^2}=3k$

Finally, $\cos A=\frac{\text{base}}{\text{hypotenuse}}=\frac{3k}{5k}=\frac{3}{5}$

$\text{Thus,}{\sin }^{2}A+{\cos }^{2}A=$
${\left(\frac{4}{5}\right)}^2+{\left(\frac{3}{5}\right)}^2$

$\Rightarrow \frac{16}{25}+\frac{9}{25}=\frac{25}{25}=1$