Question

Help for this question pls :)

Answer 1

tan(
`(A)/(2)` ) = ±
`(1)/(5)`

Explanation:

Using the trigonometric identity

tan (
`(A)/(2)` ) = ±
`\sqrt{(1-cosA)/(1+cosA) }`

Given

tanA =
`(5)/(12)` =
`(opposite)/(adjacent)`

This is a right triangle 5- 12- 13 ( with hypotenuse 13 ), then

cosA =
`(adjacent)/(hypotenuse)` =
`(12)/(13)` , then

tan (
`(A)/(2)` )

= ±
`\sqrt{(1-(12)/(13) )/(1+(12)/(13) ) }`

= ±
`\sqrt{((1)/(13) )/((25)/(13) ) }`

= ±
`\sqrt{(1)/(25) }`

= ±
`(1)/(5)`

Answer 2

Explanation:

tan(A/2)

tan(A/2)=sinA/1+cos A

tan(A/2)= 5/13÷1+12/13

tanA/2=1/5