Trigonometric EquationMedium
Question
Number of lines which are tangent to y sin x - 
& normal to y = cosx in x ∈ [0, 2π], is -
& normal to y = cosx in x ∈ [0, 2π], is - Options
A.1
B.0
C.2
D.3
Solution
Tangent to y sin x - 
at (α, sin α - ) is y - sin α + = cos α(x - α) .......(i)
Normal to y = cosx at (β, cosβ) is y - cos β =
(x - β) .......(ii)
on comparing (1) & (2)
cos α = ⇒ cos α. sinβ = 1
possible pairs of (α, β) are
only for α = 0, β =
(1) & (2) are same
at (α, sin α - ) is y - sin α + = cos α(x - α) .......(i)Normal to y = cosx at (β, cosβ) is y - cos β =
(x - β) .......(ii)on comparing (1) & (2)
cos α =
⇒ cos α. sinβ = 1possible pairs of (α, β) are
only for α = 0, β =
(1) & (2) are sameCreate a free account to view solution
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