From ncert 11 grade math ch3 important concept que...

Created on: February 1, 2026

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Question

From ncert 11 grade math ch3 important concept question form book back

Thought

Clarifying approach for NCERT math request

The user seems to want important concept questions from Chapter 3 of the NCERT Class 11 Maths book on Trigonometric Functions. However, I can't provide verbatim content from copyrighted material. Instead, I can summarize key concepts and create original practice questions to help.

Creating original questions for Trigonometric Functions

We can't provide verbatim questions from the book, but I can help by listing key concepts from the chapter and making original practice questions. These could cover topics like identities, graphs, equations, and inverse trigonometric functions. I'll add some sample questions and categorize them: basics, identities, graphs, equations, etc.

Clarifying trigonometric topics for chapter 3

Chapter 3 of Class 11 focuses on trig functions, angles, identities, graphs, and related concepts like radian measure, sum/difference formulas, and periodicity. It doesn't include inverse trig, which appears in a later chapter. I'll create NCERT-style important questions on these topics and include possible answers or hints.

Making structured materials for trigonometry

I’ll organize the materials into three sections: important concepts, a formula sheet, and NCERT-style practice questions, with three levels of difficulty (Very Short, Short, Long). I'll include original answers, hints, and general solution patterns like sin x = sin a. Also, I’ll cover transformations, domain/range, key identities, and graphs.

Thought for 26s

Answer

I can’t copy the exact “book-back” NCERT questions word-for-word (copyright), but I can give you a high-yield “Important Concepts + NCERT-style Important Questions” set for Class 11 Maths, Chapter 3 (Trigonometric Functions). If you upload a photo of the back-exercise page, I can also solve those exact questions.

Chapter 3: Must-know concepts (quick list)

  • Degree–radian conversion, angle measure on circle, arc length idea
  • Trig functions as coordinates on unit circle; signs in quadrants
  • Standard values at 0, π/6, π/4, π/3, π/20,\ \pi/6,\ \pi/4,\ \pi/3,\ \pi/2 etc.
  • Periodicity and graphs of sin,cos,tan,cot,sec,csc\sin,\cos,\tan,\cot,\sec,\csc
  • Domain & range; maxima/minima of basic trig expressions
  • Identities: Pythagorean, reciprocal, quotient
  • Compound angle: sin(A±B), cos(A±B), tan(A±B)\sin(A\pm B),\ \cos(A\pm B),\ \tan(A\pm B)
  • Double angle + simple transformations
  • General solutions of trig equations

Formula sheet (most used)

  • sin2x+cos2x=1\sin^2x+\cos^2x=1, 1+tan2x=sec2x1+\tan^2x=\sec^2x, 1+cot2x=csc2x1+\cot^2x=\csc^2x
  • sin(A±B)=sinAcosB±cosAsinB\sin(A\pm B)=\sin A\cos B\pm \cos A\sin B
  • cos(A±B)=cosAcosBsinAsinB\cos(A\pm B)=\cos A\cos B\mp \sin A\sin B
  • tan(A±B)=tanA±tanB1tanAtanB\tan(A\pm B)=\dfrac{\tan A\pm \tan B}{1\mp \tan A\tan B}
  • sin2x=2sinxcosx\sin 2x=2\sin x\cos x
  • cos2x=cos2xsin2x=12sin2x=2cos2x1\cos 2x=\cos^2x-\sin^2x=1-2\sin^2x=2\cos^2x-1
  • General solutions:
    • sinx=sinax=nπ+(1)na\sin x=\sin a \Rightarrow x=n\pi+(-1)^n a
    • cosx=cosax=2nπ±a\cos x=\cos a \Rightarrow x=2n\pi\pm a
    • tanx=tanax=nπ+a\tan x=\tan a \Rightarrow x=n\pi+a where nZn\in\mathbb Z

Important NCERT-style questions (original practice set)

A) Basic / 1-mark–2-mark

  1. Convert: (i) 150150^\circ to radians (ii) 7π6\dfrac{7\pi}{6} to degrees.
  2. Find sin(11π6), cos(7π4), tan(5π3)\sin\left(\dfrac{11\pi}{6}\right),\ \cos\left(\dfrac{7\pi}{4}\right),\ \tan\left(\dfrac{5\pi}{3}\right).
  3. If sinθ=35\sin\theta=\dfrac{3}{5} and θ\theta is in quadrant II, find cosθ,tanθ\cos\theta,\tan\theta.
  4. State domain and range of y=sinxy=\sin x and y=secxy=\sec x.
  5. Find the period of (i) sin(3x)\sin(3x) (ii) cos(x2)\cos\left(\dfrac{x}{2}\right) (iii) tan(2xπ/6)\tan(2x-\pi/6).

B) Identities (very important)

  1. Prove: 1sinxcosx=secxtanx\dfrac{1-\sin x}{\cos x}=\sec x-\tan x.
  2. Prove: (secxtanx)(secx+tanx)=1(\sec x-\tan x)(\sec x+\tan x)=1.
  3. Simplify: sinx+sin3xcosx+cos3x\dfrac{\sin x+\sin 3x}{\cos x+\cos 3x}.
  4. Prove: cosx1sinx=secx+tanx\dfrac{\cos x}{1-\sin x}=\sec x+\tan x.
  5. If sinx+cosx=2cos(xπ4)\sin x+\cos x=\sqrt2\cos\left(x-\dfrac{\pi}{4}\right), use it to find the maximum value of sinx+cosx\sin x+\cos x.

C) Compound angle / double angle (high frequency)

  1. Evaluate exactly: sin75, cos15, tan105\sin 75^\circ,\ \cos 15^\circ,\ \tan 105^\circ.
  2. Express sin(x+π/3)\sin(x+\pi/3) in terms of sinx,cosx\sin x,\cos x.
  3. If tanA=12\tan A=\dfrac{1}{2} and tanB=13\tan B=\dfrac{1}{3}, find tan(A+B)\tan(A+B).
  4. Prove: sin(x+y)sin(xy)=sin2xsin2y\sin(x+y)\sin(x-y)=\sin^2x-\sin^2y.
  5. Using double-angle, show that 1+cos2x=2cos2x1+\cos 2x=2\cos^2x.

D) Graph / domain-range based

  1. Find domain and range of y=2sin(3xπ/4)y=2\sin(3x-\pi/4).
  2. Find all x[0,2π]x\in[0,2\pi] where cosx0\cos x\ge 0.
  3. For y=tanxy=\tan x, write the interval(s) in [0,2π][0,2\pi] where it is increasing and where it is undefined.

E) Trigonometric equations (most asked)

  1. Solve in [0,2π][0,2\pi]: 2sinx=32\sin x=\sqrt3.
  2. Solve in [0,2π][0,2\pi]: cos2x=12\cos 2x=\dfrac{1}{2}.
  3. Solve (general solution): tanx=1\tan x=1.
  4. Solve (general solution): sin(2x)=sin(π3)\sin(2x)=\sin\left(\dfrac{\pi}{3}\right).
  5. Solve in [0,2π][0,2\pi]: sinx+cosx=0\sin x+\cos x=0.
  6. Solve in [0,2π][0,2\pi]: secx=2\sec x=2.
  7. Solve (general solution): cosx=cos(π6)\cos x=\cos\left(\dfrac{\pi}{6}\right).

If you tell me which exercise you mean (e.g., “Miscellaneous Exercise” or a specific exercise number), or upload a photo of the “book back” questions, I’ll mark the most important ones and give you step-by-step solutions.

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