NCERT Solutions for Class 12 Maths Inverse Trigonometry Functions Miscellaneous Exercise

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NCERT Solutions for Class 12 Maths are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of CBSE Class 12^th Maths like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.

CBSE Class 12^th is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So CBSE NCERT Solutions for Class 12^th Maths is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.

As we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the CBSE NCERT Syllabus. Thus, NCERT Solutions helps the students to solve the exercise questions as given in NCERT Books.

NCERT Solutions for Class 12 Maths Inverse Trigonometry Functions Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 1.

Find the value of cos^-1(cos13π/6).

NCERT Solutions:

Given that cos^-1(cos13π/6).

We know that cos^-1(cosx) = x if the principle value of cos^-1x is x ∊ [0, π].

Since 13π/6 ∉ [0, π], we have 

cos^-1(cos13π/6) = cos^-1(cos(2π + π/6)) = cos^-1(cos(π/6)).

Since π/6 ∊ [0, π], we have 

cos^-1(cos13π/6) = cos^-1(cos(2π + π/6)) = cos^-1(cos(π/6)) = π/6. 

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 2.

Find the value of tan^-1(tan7π/6).

NCERT Solutions:

Given that tan^-1(tan7π/6).

We know that tan^-1(tanx) = x if the principle value of tan^-1x is x ∊ (-π/2, π/2).

Since 7π/6 ∉ (-π/2, π/2), we have 

tan^-1(tan7π/6) = tan^-1(tan(π + π/6) = tan^-1(tan(π/6)).

Since π/6 ∊ (-π/2, π/2), we have 

tan^-1(tan7π/6) = tan^-1(tan(π + π/6) = tan^-1(tan(π/6)) = π/6. 

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 3.

Prove that 2sin^-1(3/5) = tan^-1(24/7).

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 4.

Prove that sin^-1(8/17) + sin^-1(3/5) = tan^-1(77/36).

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 5.

Prove that cos^-1(4/5) + cos^-1(12/13) = cos^-1(33/65).

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 6.

Prove that cos^-1(12/13) + sin^-1(3/5) = sin^-1(56/65).

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 7.

Prove that tan^-1(63/16) = sin^-1(5/13) + cos^-1(3/5).

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 8.

Prove that tan^-1(1/5) + tan^-1(1/7) + tan^-1(1/3) + tan^-1(1/8) = π/4.

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 9.

Prove that tan^-1(√x) = (1/2)cos^-1((1 – x)/(1 + x)), x ∊ [0, 1].

NCERT Solutions:

LHS = tan^-1(√x) = (1/2)(2tan^-1(√x)) = (1/2)cos^-1((1 – x)/(1 + x)) = RHS

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 10.

Prove that .

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 11.

Prove that .

NCERT Solutions:

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 12.

Prove that 9π/8 – (9/4)sin^-1(1/3) = (9/4)sin^-1(2√2 /3).

NCERT Solutions:

LHS = 9π/8 – (9/4)sin^-1(1/3) = (9/4)(π/2 – sin^-1(1/3)) = (9/4)(cos^-1(1/3)) = (9/4)sin^-1(2√2 /3) = RHS.

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 13.

Solve the equation 2tan^-1(cos x) = tan^-1(2cosec x).

NCERT Solutions:

Given that 

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 14.

Solve the equation tan^-1((1 – x)/(1 + x)) = (1/2)tan^-1(x), x > 0.

NCERT Solutions:

Given that 

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 15.

sin(tan^-1x), |x| < 1 is equal to 

NCERT Solutions:

Given that sin(tan-1x) = sin(sin-1(x/√(1 + x²))) = x/√(1 + x²). Correct option is D. 

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 16.

Solve the equation sin^-1(1 – x) – 2sin^-1(x) = π/2

(A) 0, 1/2     (B) 1, 1/2     (C) 0,      (D) 1/2

NCERT Solutions:

Given that

Put x = sin y, then

Now, at x = 1/2, we have Thus

Thus, x = 1/2 is not a solution. Correct option is C.

NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc Exercise: Ques No 17.

tan^-1(x/y) – tan^-1((x – y)/(x + y)) is equal to 

(A) π/2     (B) π/3     (C) π/4,      (D) -3π/4

NCERT Solutions:

Given that

Correct option is C.

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