Question

Question #6e2a4

Answer 1

See the answer below....

Explanation:

`sectheta-sintheta cdot tantheta`
`=1/costheta-sintheta cdot sintheta/costheta`
`=(1-sin^2theta)/costheta`
`=cos^2theta/costheta` [`"as "sin^2theta+cos^2theta=1`]
`=costheta`

Proved

Hope it helps....
Thank you...

Answer 2

`"see explanation"`

Explanation:

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

`•color(white)(x)sin^2x+cos^2x=1`

`•color(white)(x)secx=1/cosx" and "tantheta=sintheta/costheta`

`"consider the left hand side"`

`sectheta-sinthetatantheta`

`=1/costheta-sinthetaxxsintheta/costheta`

`=1/costheta-sin^2theta/costheta`

`=(1-sin^2theta)/costheta=cos^2theta/costheta`

`=(cancel(costheta)costheta)/cancel(costheta)`

`=costheta=" right hand side "rArr"proven"`