Question

If tan theta =½ and theta is an acute angle what is cos theta​

Answer 1

cosθ =
`(2√(5) )/(5)`

Explanation:

given

tanθ =
`(1)/(2)` =
`(opposite)/(adjacent)`

that is opposite = 1 , adjacent = 2

we have a right triangle with legs 1 and 2

use Pythagoras' identity to find the hypotenuse h

h² = 1² + 2² = 1 + 4 = 5 ( take square root of both sides )

h =
`√(5)`

then

cosθ =
`(adjacent)/(hypotenuse)` =
`(2)/(√(5) )`

rationalise the denominator by multiplying numerator/denominator by
`√(5)`

cosθ =
`(2√(5) )/(√(5)(√(5)) )` =
`(2√(5) )/(5)`