Question

If sin²A =1/2,then find the value of cos²A

Answer 1

Answer:

Given that :-)

${sin}^{2} A = \frac{1}{2}$

Also we know that

property in trigonometric ratios sin and Cos is:-)

${sin}^{2}A + {cos}^{2} A = 1$

Now

Using the property and given we can calculate the required ratio as:-)

$\frac{1}{2} + {cos}^{2} A = 1 \\ \implies \: {cos}^{2} A= 1 - \frac{1}{2} \\ \implies {cos}^{2} A = \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{Answer}}$

So, required value of:

${cos}^{2} A = \frac{1}{2}$

Answer 2

$\large \underline{ \underline{ \sf \: Answer : \: \: \: }}$

$\to \sf { \cos}^{2} A= \frac{1}{ \: 2 \: }$

$\large \underline{ \underline{ \sf \: Explaination : \: \: \: }}$

Given ,

$\star \: \: \sf { \sin}^{2} A = \frac{1}{ \: 2 \: }$

We know that ,

$\large \fbox{ \fbox{\sf { \sin}^{2} A + { \cos}^{2} A = 1 }}$

$\to \sf \frac{1}{ \: 2 \: } + { \cos}^{2} A= 1 \\ \\ \to \sf { \cos}^{2} A= 1 - \frac{1}{ \: 2 \: } \\ \\ \to \sf { \cos}^{2} A= \frac{1}{ \: 2 \: }$