Question

If `tanA+secA=2` then find `cosA`?

Answer 1

`cosA=4/5`

Explanation:

`tanA+secA=2`

Substituting the definition of `tan` and `sec` gives us:
`sinA/cosA+1/cosA=2`

Multiplying by `cosA`:
`sinA+1=2cosA`

`:. sinA=2cosA - 1`
`:. sin^2A=(2cosA - 1)^2`

Using the fundamental identity `sin^2X+cos^2X-=1`
`1-cos^2A=(2cosA - 1)^2`
`:. 1-cos^2A=4cos^2A-4cosA+1`
`:. 5cos^2A-4cosA = 0`
`:. cosA(5cosA-4) = 0`
`cosA=0` or `5cosA-4 = 0 => cosA=4/5`

We were told that A is an acute angle, so we can eliminate the solution `cosA=0`

Hence, `cosA=4/5`