Question

If cos 2A = 7 /9 , show that SinA = 1/3​

Answer 1

see explanation

Explanation:

using the identity

cos2A = 1 - 2sin²A , then

1 - 2sin²A =
`(7)/(9)` ( subtract 1 from both sides )

- 2sin²A = -
`(2)/(9)` ( divide both sides by - 2 )

sin²A =
`(1)/(9)` ( take square root of both sides )

sinA =
`\sqrt{(1)/(9) }` =
`(1)/(3)`

Answer 2

Hello There ~

`\longrightarrow \sf \cos(2a) = (7)/(9)`

`\longrightarrow \sf1 - 2 \sin {}^(2) (a) = (7)/(9)`

[ cos 2a = 1 - 2sin²a ]

`\longrightarrow \sf 2{sin}^(2) (a) = 1 - (7)/(9)`

`\longrightarrow \sf2 {sin}^(2) (a) = (9 - 7)/(9)`

`\longrightarrow \sf2 {sin}^(2) (a) = (2)/(9)`

`\longrightarrow \sf {sin}^(2) (a) = (1)/(9)`

`\longrightarrow \sf {sin(a) = (1)/(3) }`

Hope it helps -',...,'-