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Question

If cosecc θ = 10 then sec θ = ?

(a)  310  (b)  103 (c)  110 (d)  210


Solution

ABC is a right-angled triangle.

Given: cosec θ=10

But sinθ=1cosecθ=110

Also, sinθ=Opposite sideHypotenuse side=BCACBCAC=110

Thus BC=k  and  AC=10k

Using Pythagoras theorem in ABC, we have,

AC2=AB2+BC2AB2=AC2BC2AB2=(10k)2(k)2AB2=9k2AB=3ksec θ=ACAB=10k3k=103

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