Question

If tanA=3/7 find the values of 2cosAsinA-cosA/1+sin^2A-sinA-cos^2A?

If `tanA = 3/7` find the value of `2cosAsinA-cosA//1+sin^2A-sinA-cos^2A`?

Answer 1

Plug into calculator:

`2(7/sqrt(3^2 + 7^2)(3/sqrt(3^2 + 7^2))-(7/sqrt(3^2 + 7^2)/1 + (3/sqrt(3^2 + 7^2))^2 - (3/sqrt(3^2 + 7^2)) - (7/sqrt(3^2 + 7^2))^2`

Explanation:

If `tan A = 3/7` then the hypotenuse of the triangle is =
`sqrt(3^2 + 7^2)`

Therefore since `cos = a/h and sin = o/h` then `cos A = 7/sqrt(3^2 + 7^2)` and `sinA = 3/sqrt(3^2 + 7^2)`

From this knowledge you should then be able to work out the rest on your calculator using:

`2(7/sqrt(3^2 + 7^2)(3/sqrt(3^2 + 7^2))-(7/sqrt(3^2 + 7^2)/1 + (3/sqrt(3^2 + 7^2))^2 - (3/sqrt(3^2 + 7^2)) - (7/sqrt(3^2 + 7^2))^2`