Ncert exemplar class 12 maths solutions pdf

Evaluate tan[tan⁻¹(d/(1+a₁a₂)) + tan⁻¹(d/(1+a₂a₃)) + …] | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q19 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question If a₁, a₂, a₃, … , aₙ are in arithmetic progression with common difference d, evaluate: \[ \tan\Big[ \tan^{-1}\!\left(\frac{d}{1+a_1a_2}\right) + \tan^{-1}\!\left(\frac{d}{1+a_2a_3}\right) + \cdots + \tan^{-1}\!\left(\frac{d}{1+a_{n-1}a_n}\right) \Big] \] [NCERT EXEMPLAR …

Evaluate tan[tan⁻¹(d/(1+a₁a₂)) + tan⁻¹(d/(1+a₂a₃)) + …] | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q19 Read More »

NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Free Online Tests Video Tutorials Question Show that \[ \tan\left(\frac{1}{2}\sin^{-1}\frac{3}{4}\right) = \frac{4 – \sqrt{7}}{3} \] and justify why the other value \[ \frac{4 + \sqrt{7}}{3} \] is ignored. [NCERT EXEMPLAR 2.3, Q.18, Page 37] Solution We have, \[ \tan\left(\frac{1}{2}\sin^{-1}\frac{3}{4}\right) = \frac{4 – \sqrt{7}}{3} \] Let …

Show that tan(½ sin⁻¹(3/4)) = (4 – √7)/3 and justify why the other value (4 + √7)/3 is ignored | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q18 Read More »

Find the value of 4 tan⁻¹(1/5) − tan⁻¹(1/239) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q17 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Find the value of \[ 4\tan^{-1}\left(\frac{1}{5}\right) – \tan^{-1}\left(\frac{1}{239}\right) \] [NCERT EXEMPLAR Ex 2.3, Question 17, Page 37] Free Online Tests Video Tutorials Solution We have: \[ 4\tan^{-1}\left(\frac{1}{5}\right) …

Find the value of 4 tan⁻¹(1/5) − tan⁻¹(1/239) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q17 Read More »

Prove that tan⁻¹(1/4) + tan⁻¹(2/9) = sin⁻¹(1/√5) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q16 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Prove that \[ \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) = \sin^{-1}\left(\frac{1}{\sqrt{5}}\right) \] [NCERT EXEMPLAR Ex 2.3, Question 16, Page 36] Free Online Tests Video Tutorials Solution Let \[ \tan^{-1}\left(\frac{1}{4}\right) = x …

Prove that tan⁻¹(1/4) + tan⁻¹(2/9) = sin⁻¹(1/√5) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q16 Read More »

NCERT Class 12 Mathematics Solutions – Exercise 2.3 Question 15 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Free Online Tests Video Tutorials Question Show that \[ \sin^{-1}\left(\frac{5}{13}\right) + \cos^{-1}\left(\frac{3}{5}\right) = \tan^{-1}\left(\frac{63}{16}\right) \] [NCERT EXEMPLAR Ex 2.3, Question 15, Page 36] Solution Let \[ \sin^{-1}\left(\frac{5}{13}\right) = x \] Then, \[ \sin x = …

Show that sin⁻¹(5/13) + cos⁻¹(3/5) = tan⁻¹(63/16) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q15 Read More »

NCERT Class 12 Mathematics Solutions – Exercise 2.3 Question 14 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Prove that \[ \sin^{-1}\left(\frac{8}{17}\right) + \sin^{-1}\left(\frac{3}{5}\right) = \sin^{-1}\left(\frac{77}{85}\right) \] [NCERT EXEMPLAR Ex 2.3, Question 14, Page 36] Free Online Tests Video Tutorials Solution Let \[ \sin^{-1}\left(\frac{8}{17}\right) = \theta_1, \quad \sin^{-1}\left(\frac{3}{5}\right) = \theta_2 \] Then, …

Prove that sin⁻¹(8/17) + sin⁻¹(3/5) = sin⁻¹(77/85) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q14 Read More »

NCERT Class 12 Mathematics Solutions – Exercise 2.3 Question 13 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Find the simplified form of \[ \cos^{-1}\left(\frac{3}{5}\cos x + \frac{4}{5}\sin x\right), \quad x \in \left[-\frac{3\pi}{4}, \frac{\pi}{4}\right] \] [NCERT EXEMPLAR Ex 2.3, Question 13, Page 36] Free Online Tests Video Tutorials Solution We have, \[ …

Find the simplified form of cos⁻¹((3/5)cos x + (4/5)sin x) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q13 Read More »

NCERT Class 12 Mathematics Solutions – Exercise 2.3 Question 12 NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Prove that \[ \tan^{-1}\left(\frac{\sqrt{1+x^2} + \sqrt{1-x^2}}{\sqrt{1+x^2} – \sqrt{1-x^2}}\right) = \frac{\pi}{4} + \frac{1}{2}\cos^{-1}x^2 \] [NCERT EXEMPLAR 2.3, Q.12, Page 36] Free Online Tests Video Tutorials Solution We have, \[ \tan^{-1}\left(\frac{\sqrt{1+x^2} + \sqrt{1-x^2}}{\sqrt{1+x^2} – \sqrt{1-x^2}}\right) = …

Prove that tan⁻¹((√(1+x²)+√(1−x²))/(√(1+x²)−√(1−x²))) = π/4 + ½ cos⁻¹ x² | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q12 Read More »

NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Solve the equation \[ \cos(\tan^{-1}x) = \sin(\cot^{-1}\frac{3}{4}) \] [NCERT Exemplar 2.3, Question 11, Page 36] Free Online Tests Video Tutorials Solution We have: \[ \cos(\tan^{-1}x) = \sin(\cot^{-1}\frac{3}{4}) \] Using inverse trigonometric identities: \[ \cos(\tan^{-1}x) = \frac{1}{\sqrt{x^2 + 1}}, \quad \sin(\cot^{-1}\frac{3}{4}) = \frac{4}{5} \] Let …

Solve the equation cos(tan⁻¹ x) = sin(cot⁻¹ 3/4) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q11 Read More »

NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions Question Show that \[ \cos\left(2 \tan^{-1}\frac{1}{7}\right) = \sin\left(4 \tan^{-1}\frac{1}{3}\right) \] [NCERT Exemplar 2.3, Question 10, Page 36] Free Online Tests Video Tutorials Solution We have: \[ \cos\left(2 \tan^{-1}\frac{1}{7}\right) = \sin\left(4 \tan^{-1}\frac{1}{3}\right) \] Using formulas for double angle of arctan and arccos: \[ \cos\Big[\cos^{-1}\frac{1-(1/7)^2}{1+(1/7)^2}\Big] = \sin\Big[2 …

Show that cos(2 tan⁻¹(1/7)) = sin(4 tan⁻¹(1/3)) | NCERT EXEMPLAR Class 12 Maths Ex 2.3 Q10 Read More »