Question

How do you verify the identify `costhetacottheta+sintheta=csctheta`?

Answer 1

`"see explanation"`

Explanation:

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

`•color(white)(x)cottheta=costheta/sintheta" and "csctheta=1/sintheta`

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

`"consider the left side"`

`costhetaxxcostheta/sintheta+sintheta`

`=cos^2theta/sintheta+sin^2theta/sintheta`

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

`=1/sintheta=csctheta=" right side "rArr"verified"`

Answer 2

see below

Explanation:

L.H.S: `costhetaxxcot theta +sin theta`
=`cos theta xx(frac{cos theta}sin theta) +sin theta`
=`cos^2theta//sin theta +sin theta`
=`frac{cos^2 theta +sin^2 theta}sin theta`
=`1//sin theta`
=`"cosec "theta` which is the R.H.S