Question

Complete the following activity to prove:

cotθ + tanθ = cosecθ × secθ

Activity:

L.H.S. = cotθ + tanθ

= `square/sin theta xx sin theta/cos theta`

= `(square + square)/(sin theta * cos theta)`

= `1/(sin theta * cos theta)`       ...(∵ sin²θ + cos²θ = 1)

= `1/sin theta xx 1/cos theta`

= `square xx sec theta`

∴ L.H.S. = R.H.S.

∴ cotθ + tanθ = cosecθ × secθ

Answer 1

L.H.S. = cotθ + tanθ

= \[\frac{\boxed{\text{cosθ}}}{\text{sinθ}}\] `xx sin theta/cos theta`

= \[\frac{\boxed{\text{cos}^2 θ} + \boxed{\text{sin}^2θ}}{\text{sin θ . cos θ}}\]

= `1/(sin theta * cos theta)`    (∵ sin²θ + cos²θ = 1)

= `1/sin theta xx 1/cos theta`

= \[\boxed{\text{cosec θ}}\] × secθ

∴ L.H.S. = R.H.S.

∴ cotθ + tanθ = cosecθ × secθ