Question

cosA=⅖,find the value of 4+4tan²A​

Answer 1

Answer:

The value of 4 + 4 tan²A is 25.

Step-by-step explanation:

The value of cos A = $\frac{2}{5}$.

Compute the value of sin²A as follows:

$sin^{2}A+cos^{2}A=1\\sin^{2}A+(\frac{2}{5} )^{2}=1\\sin^{2}A=1-\frac{4}{25}\\ sin^{2}A=\frac{21}{25}$

Compute the value of 4 + 4 tan²A as follows:

$4+4tan^{2}A=4+(4\times\frac{sin^{2}A}{cos^{2}A} )=4+(4\times \frac{21/25}{4/25})=4+21=25$

Thus, the value of 4 + 4 tan²A is 25.

Answer 2

Answer:

cos A = 2/5

Using the identity cos^2 A + sin^2 A = 1

(2/5)2 + sin^2 A = 1

Sin^2 A = 1 - 4/25

Finally we get sin A as root 21/ 5

tan A = sin A/cos A

So, on putting the value of tan A

We get,

4 + 4 * 21/5 * 25/4

4 + 21 = 25

HOPE THAT THIS WAS HELPFUL!!!!

Step-by-step explanation: