Question

To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.

Activity:

L.H.S. = `square`

= `square/(sinθ) + (sinθ)/(cosθ)`

= `(cos^2θ + sin^2θ)/square`

= `1/(sinθ.cosθ)`   ...`[cos^2θ + sin^2θ = square]`

= `1/(sinθ) xx 1/square`

= `square`

= R.H.S.

Answer 1

L.H.S. = \[\boxed{\text{cot} \phantom{.} θ + \text{tan} \phantom{.}θ}\]

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

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

= `1/(sinθ.cosθ)`   ...[cos²θ + sin²θ = \[\boxed{1}\]]

= \[\frac{1}{\text{sin}θ} \times \frac{1}{\boxed{\text{cos}θ}}\]

= \[\boxed{\text{cosec} \phantom{.}θ \times \text{sec} \phantom{.}θ}\]

= R.H.S.