Differentiation Class 12 OP Malhotra Exe-8G ISC Maths Solutions Ch-8 Solutions. In this article you would learn about differentiation by transformation . Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

 Differentiation Class 12 OP Malhotra Exe-8G ISC Maths Solutions Ch-8

Board	ISC
Publications	S Chand
Subject	Maths
Class	12th
Chapter-8	Differentiation
Writer	OP Malhotra
Exe-8(G)	differentiation by transformation

Exercise- 8G

Differentiation Class 12 OP Malhotra Exe-8G Solution

Que-1: (i) cos^-1(cos x)
(ii) tan^-1 (cot x)

Sol: (i) Let y = cos^-1(cos x) = x
[∵ cos^-1(cos θ) = θ ∀ θ ∈ [ 0, π]]
Diff. both sides w.r.t. x ; we have
dy/dx = 1

(ii) Let y = tan^-1(cot x)
= tan^-1[tan(π/2 – x)]=π/2 – x
Diff. both sides w.r.t. x ; we have
dy/dx= 0 – 1 = – 1

Que-2: (i) tan^-1(sin x/1+cos x)
(ii) tan^-1(1-cos x/sin x)

Sol:

Que-3: tan^-1(cos x – sin x/cos x + sin x)

Sol:

Que-4: cot^-1(cos x/1+sin x)

Sol:

Que-5: sin^-1(√(1-cos 2x /2))

Sol: Let y = sin^-1(√(1-cos 2x /2))
= sin^-1(√(2 sin²x /2)) = sin^-1(sin x) = x
∴ dy/dx = 1

Que-6: sin^-1(√(1-x²))

Sol:

Que-7: sin^-1(√1/(1+x²))

Sol:

Que-8: cos^-1((1-x²)/(1+x²))

Sol:

Que-9: tan^-1((3x-x²)/(1-3x²))

Sol:

Que-10: sin^-1((2x)/(1+x²))

Sol:

Que-11: cos^-1 (2x² – 1)

Sol: Let y = cos^-1 (2x² – 1)
put x = cos θ ⇒ θ = cos^-1x
∴ y = cos^-1(2 cos²θ – 1)
∴ y = cos^-1 (cos 2θ)
⇒ y = 2θ = 2 cos^-1x
Diff. both sides w.r.t. x, we have
∴ dy/dx= -2/√(1-x²)

Que-12: sin^-1 (3x – 4x³)

Sol: Let y = sin^-1 (3x² – 4x³)
put x = sin θ ⇒ θ = sin^-1x
∴ y = sin^-1(3sin θ – 4sin³ θ)
= sin^-1(sin 3θ) = 3θ = 3
Diff. both sides w.r.t. x, we have
∴ dy/dx= 3/√(1-x²)

Que-13: cot^-1 (1 – x²/2x)

Sol:

Que-14: cosec^-1 (1 + x²/2x)

Sol:

Que-15: sin^-1 (1 – x²/1 + x²)

Sol:

Que-16: sec^-1 (x²+1/x²-1)

Sol:

Que-17: (i) tan^-1 (√(1+x/1-x))
(ii) cot^-1 (√(1+x/1-x))

Sol:

Que-18: (i) cos^-1 (√(1+x/2))
(ii) cos^-1 (√(1-x²/2))
(iii) sin^-1 (√(1+x²/2))
(iv) cos^-1 (√(1+x²/2))

Sol:

Que-19: tan^-1 (x/√a²-x²)

Sol:

Que-20: tan^-1 (√(1-x/1+x))

Sol:

Que-21: tan^-1 (x/(1+√(1-x²)))

Sol:

Que-22: tan^-1 (√a-√x/1+√ax)

Sol:

Que-23: tan^-1 (√2-x/2+x)

Sol:

Que-24: sin^-1 ((2^x+1)/(1+4^x))

Sol:

Que-25: (i) tan^-1 (√(1+x²) + x)
(ii) cot^-1 (√(1+x²) – x)

Sol:

Que-26: (i) tan^-1 ((√(1+x²) + 1)/x)
(ii) tan^-1 ((√(1+a²x²) – 1)/ax)

Sol:

Que-27: sin²[cot^-1 (√1-x/1+x)]

Sol:

–: End Differentiation Class 12 OP Malhotra Exe-8G ISC Math Ch-8 Solution :–

Return to :- OP Malhotra ISC Class-12 S Chand Publication Maths Solutions
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