Without using trigonometric tables, evaluate the following:
cosec 17°30′sec 72° 30′\dfrac{\text{cosec 17°30}'}{\text{sec 72° 30}'}sec 72° 30′cosec 17°30′.
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Solving,
⇒cosec 17° 30′sec 72° 30′⇒cosec (90° - 72° 30′)sec 72° 30′As, cosec (90 - θ) = sec θ⇒sec 72° 30′sec 72° 30′⇒1.\Rightarrow \dfrac{\text{cosec 17° 30}'}{\text{sec 72° 30}'} \\[1em] \Rightarrow \dfrac{\text{cosec (90° - 72° 30}')}{\text{sec 72° 30}'} \\[1em] \text{As, cosec (90 - θ) = sec θ} \\[1em] \Rightarrow \dfrac{\text{sec 72° 30}'}{\text{sec 72° 30}'} \\[1em] \Rightarrow 1.⇒sec 72° 30′cosec 17° 30′⇒sec 72° 30′cosec (90° - 72° 30′)As, cosec (90 - θ) = sec θ⇒sec 72° 30′sec 72° 30′⇒1.
Hence, cosec 17° 30′sec 72° 30′=1\dfrac{\text{cosec 17° 30}'}{\text{sec 72° 30}'} = 1sec 72° 30′cosec 17° 30′=1.
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