If sec θ = cosec θ and 0° ≤ θ ≤ 90°, find the value of θ.
Given,
⇒sec θ = cosec θ⇒1cos θ=1sin θ⇒sin θcos θ=1⇒tan θ=1⇒tan θ = tan 45°⇒θ=45°.\Rightarrow \text{sec θ = cosec θ} \\[1em] \Rightarrow \dfrac{1}{\text{cos θ}} = \dfrac{1}{\text{sin θ}} \\[1em] \Rightarrow \dfrac{\text{sin θ}}{\text{cos θ}} = 1 \\[1em] \Rightarrow \text{tan θ} = 1 \\[1em] \Rightarrow \text{tan θ = tan 45°} \\[1em] \Rightarrow \text{θ} = 45°.⇒sec θ = cosec θ⇒cos θ1=sin θ1⇒cos θsin θ=1⇒tan θ=1⇒tan θ = tan 45°⇒θ=45°.
Hence, θ = 45°.
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