Continuity and DifferentiabilityHard
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
View Solution FreeMore Continuity and Differentiability Questions
If x = a sin3 t, y = a cos3 t then dy/dx equals-...If (cosx)y = (siny)x, then equals -...If y2 = P(x) is a polynomial of degree 3, then 2 is equal to...If function f(x) = , is continuous at x = a, then the value of f(a) is -...If x3 − y3 + 3xy2 − 3x2y + 1 = 0, then at (0,1) dy/dx equals-...