Question

Question #b88bf

Answer 1

See below

Explanation:

To Prove
`cottheta+tantheta=sectheta csctheta`

L.H.S.
`=cottheta+tantheta`

`because cottheta=costheta/sintheta "and" tantheta=sintheta/costheta`

`=costheta/sintheta+sintheta/costheta`
Take LCM `Sinthetacostheta`
`=(cos^2theta+sin^2theta)/(sinthetacostheta)`
`=1/(sinthetacostheta)`

`because 1/sintheta=csctheta ""and" 1/costheta=sectheta`

`=secthetacsctheta`

Answer 2

`"see explanation"`

Explanation:

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

#•color(white)(x)cottheta=costheta/sintheta" and "tantheta=sintheta/costheta"#

`•color(white)(x)cosectheta=1/sintheta" and "sectheta=1/costheta"`

`•color(white)(x)cos^2theta+sin^2theta=1`

`rArrcottheta+tantheta`

`=>costheta/sintheta+sintheta/costheta`

`=>(cos^2theta+sin^2theta)/(sintheta×costheta)`

`=>1/(sinthetacostheta)=1/sintheta×1/costheta=csctheta×sectheta`