Question

What is cost(sect-cost)? (Trigonometric )

Answer 1

`cost(sect-cost)=sin^2t`

Explanation:

We know that,

`color(red)((1)sin^2x+cos^2x=1=>sin^2x=1-cos^2x`

`color(red)((2)cosx=1/secx=>color(blue)(cosx*secx=1`

We have,

`cost(sect-cost)=color(blue)(cost*sect)-costcost`

Using `(2)`,we get

`cost(sect-cost)=color(blue)(1)-cos^2t`

Using `(1)`,we get

`cost(sect-cost)=color(red)(sin^2t`

Answer 2

`sin^2t`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)secx=1/cosx`

`•color(white)(x)sin^2x+cos^2x=1`

`rArrcost(sect-cost)`

`=cancel(cost)^1xx1/cancel(cost)^1-cos^2t`

`=1-cos^2t=sin^2t`