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Question

If cosec θcot θ=12,0<θ<90 then cos θ is equal to _______. 
  1. 53
  2. 35
  3. 35
  4. 53


Solution

The correct option is B 35

Given:
cosec θcot θ=12 --------- (i)
Using identity
 cosec2 θcot2 θ=1
(cosecθ+cotθ)(cosecθcotθ)=1 -------(ii)

Substituting, (i) in (ii) we get,
(cosec θ+cot θ)(12)=1 

(cosec θ+cot θ)=2 ----------- (iii)

On adding (i) and (iii), 
2cosecθ=12+2=52cosecθ=54

Since, cosec θ=1sin θ,
sinθ=45sin2θ=4252=1625

By the identity, sin2 θ=1cos2 θ,
1cos2θ=1625cos2θ=11625=925
cos θ=±35

0<θ<90,cos θ=35

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