These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2
Question 1.
Evaluate the following:
Solution:
Question 2.
Choose the correct option and justify your choice:
(i) \(\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}\) =
(A) sin 600 (B) cos 60°
(C) tan 60° (D) sin 300
(ii) \(\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}\) =
(A) tan 90° (B) 1
(C) sin 450 (D) O
(iii) sin 2A = 2 sin A is true when A =
(A) 00 (B) 30°
(C) 45° (D) 60°
(iv) \(\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}\) =
(A) cos 60° (B) cos 60°
(C) tan 60° (D) sin 300
Solution:
(i) We have given,
(ii) We have given,
(iii) We have given,
Therefore,
sin 2 A = 2 sin A is true only when A = 0°
∴ correct option is (A)
(iv) We have given,
Question 3.
If tan (A + B) = √3 and tan (A – B) = \(\frac { 1 }{ \surd 3 }\); 0° < A + B ≤ 90°; A > B, find A and B.
Solution:
We have given
tan (A + B) = √3
⇒ tan (A + B) = tan 60°
⇒ A + B = 60° … (i)
tan (A – B) = \(\frac { 1 }{ \surd 3 }\)
⇒ tan (A – B) = tan 30°
⇒ A – B = 30° … (ii)
Adding equation (i) and (ii), we get
2A = 90° ⇒ A = 45°
Putting the velue of A in equation (i), we get
45° + B = 60° ⇒ B = 60° – 45° = 15°
Therefore A = 45° and B = 15°
Question 4.
State whether the following statements are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Solution:
(i) False, because if A = 60° and B = 30° then
sin (A + B) = sin (60° – 30°)
= sin 90° = 1
sin A + sin B = sin 60° + sin 30°
= \(\frac{\sqrt{3}}{2}+\frac{1}{2}\) = \(\frac{\sqrt{3}+1}{2}\)
∴ sin (A + B) ≠ sin A + sin B, when A = 60° and B = 30°
(ii) True, because the value of sin θ increases as θ increases from θ to 90°, but when θ increases from 90° to 180° then the value of sin 0 decreases.
(iii) False, because the value of cos θ decreases as θ increases from 0 to 90°.
(iv) False, because sin θ = cos θ is true only when θ = 45°. It is not true for all values of θ,
(iv) True, because cot 0° = \(\frac { 1 }{ 0 }\) = not defined.