DifferentiationHard
Question
The differential coefficient of sin-1
w.r.t. cos-1 
is
w.r.t. cos-1 isOptions
A.1 ∀ t > 0
B.- 1 ∀ t < 0
C.1 ∀ t ∈ R
D.none of these
Solution
y = sin-1 
, z = cos-1 
∵ - 1 <
< 1 and 0 < 
≤ 1 ∀ t ∈ R
let sin-1
= θ ⇒ θ ∈ (- π/2, π/2)
= sin θ ⇒ cos θ = 
(i) if θ ∈
, then
y = θ, z = θ
⇒
= 1
(ii) if θ ∈
, then
y = θ, z = - θ ⇒
= - 1
, z = cos-1 ∵ - 1 <
< 1 and 0 < ≤ 1 ∀ t ∈ Rlet sin-1
= θ ⇒ θ ∈ (- π/2, π/2) = sin θ ⇒ cos θ = (i) if θ ∈
, then y = θ, z = θ
⇒
= 1(ii) if θ ∈
, theny = θ, z = - θ ⇒
= - 1Create a free account to view solution
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