Question

Someone please answer this question
I will mark as brainliest ​

Answer 1

Given: tan A = 1/2

To find: (cosA/sinA) + sinA/(1+cosA)

Solution:

$= \frac{cos A (1 + cos A ) + {sin}^{2}A }{sin A (1 + cos A )}$

$= \frac{cos A \: + {cos}^{2}A \: + {sin}^{2}A}{sin A(1 + cosA)}$

$= \frac{1 + cos A }{sinA \: (1 + cosA)}$

$= \frac{1}{sin A } \:$

Now, tan A = 1/2

P/B = 1/2

P = 1x, B = 2x

H^2 = P^2 + B^2

H = √( 5x^2)

H = x√5

Now, sin A = P/H

sin A = x/x√5

sin A = 1/√5

$= > \frac{1}{sin A } = \sqrt{5}$