Chapter 8 · Trigonometry

NCERT Class 10 Maths Exercise 8.2

All 4 questions of NCERT Class 10 Maths Exercise 8.2 (Trigonometry), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Evaluate ​the ​following: ​

   1. (i)$\sin 60^{\circ }\cos 30^{\circ }+\sin 30^{\circ }\cos 60^{\circ }$ ​
   2. (ii)$2{\tan }^{2}45^{\circ }+{\cos }^{2}30^{\circ }-{\sin }^{2}60^{\circ }$ ​
   3. (iii)$\frac{\cos 45^{\circ }}{\sec 30^{\circ }+\csc 30^{\circ }}$ ​
   4. (iv)$\frac{\sin 30^{\circ }+\tan 45^{\circ }-\csc 60^{\circ }}{\sec 30^{\circ }+\cos 60^{\circ }+\cot 45^{\circ }}$
   5. (v)$\frac{5{\cos }^{2}60^{\circ }+4{\sec }^{2}30^{\circ }-{\tan }^{2}45^{\circ }}{{\sin }^{2}30^{\circ }+{\cos }^{2}30^{\circ }}$.
   Show answer

   (i) $1$; (ii) $2$; (iii) $\frac{3\sqrt{2}-\sqrt{6}}{8}$; (iv) $\frac{43-24\sqrt{3}}{11}$; (v) $\frac{67}{12}$.

   Step-by-step solution →
2. Q2
   Choose the correct option ​and justify ​your choice:

   1. (i)$\frac{2\tan 30^{\circ }}{1+{\tan }^{2}30^{\circ }}=$ ​(A) $\sin 60^{\circ }$ ​(B) $\cos 60^{\circ }$ (C) $\tan 60^{\circ }$ ​(D) $\sin 30^{\circ }$. ​
   2. (ii)$\frac{1-{\tan }^{2}45^{\circ }}{1+{\tan }^{2}45^{\circ }}=$ (A) $\tan 90^{\circ }$ (B) $1$ (C) $\sin 45^{\circ }$ (D) $0$.
   3. (iii)$\sin 2A=2\sin A$ is ​true when $A=$ (A) $0^{\circ }$ (B) $30^{\circ }$ ​(C) $45^{\circ }$ (D) $60^{\circ }$.
   4. (iv)$\frac{2\tan 30^{\circ }}{1-{\tan }^{2}30^{\circ }}=$ (A) $\cos 60^{\circ }$ (B) $\sin 60^{\circ }$ (C) $\tan 60^{\circ }$ (D) $\sin 30^{\circ }$.
   Show answer

   (i) (A) $\sin 60^{\circ }$; (ii) (D) $0$; (iii) (A) $0^{\circ }$; (iv) (C) $\tan 60^{\circ }$.

   Step-by-step solution →
3. Q3
   If $\tan (A+B)=\sqrt{3}$ ​and $\tan (A-B)=\frac{1}{\sqrt{3}}$; $0^{\circ }<A+B\le 90^{\circ }$; $A>B$, find $A$ ​and $B$.
   Show answer

   $A=45^{\circ }$ and $B=15^{\circ }$.

   Step-by-step solution →
4. Q4
   State whether the ​following are ​true ​or false. Justify your answer.

   1. (i)$\sin (A+B)=\sin A+\sin B$.
   2. (ii)The value of $\sin \theta$ increases as $\theta$ increases.
   3. (iii)The value of $\cos \theta$ ​increases as $\theta$ ​increases.
   4. (iv)$\sin \theta =\cos \theta$ for ​all values of $\theta$.
   5. (v)$\cot A$ is not defined for $A=0^{\circ }$.
   Show answer

   (i) False; (ii) True; (iii) False; (iv) False; (v) True.

   Step-by-step solution →