In this post, you will find the NCERT solutions for class 10 maths ex 8.2. These solutions are based on the latest curriculum of NCERT Maths class 10.
NCERT Solutions for Class 10 Maths Ex 8.2
1. Evaluate:
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan2 45° + cos2 30°
– sin2 60°
(iii)
(v)
Solution: (i) sin 60° cos 30° + sin 30° cos
60°
=
= ¾
+ ¼ = 4/4 = 1
(ii) 2 tan2 45° + cos2 30°
– sin2 60°
=
= 2
+ ¾ - ¾ = 2
(iii)
=
=
=
=
(iv)
=
=
=
(v)
=
2. Choose the correct option
and justify your choice:
(i)
(ii)
(A) tan 90° (B) 1 (C) sin 45° (D) 0
(iii) sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°
(iv)
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°
Solution: (i) (A)
=
(ii) (D)
= (1 –
1)/(1 + 1)
= 0/2 = 0
(iii) (A) If A = 0, then
Sin
2A = sin 0° = 0 and 2 sin A = 2 sin 0°
= 2
× 0 = 0
Sin 2A = 2 sin A when A = 0
(iv) (C)
=
3. If tan (A + B) = √3 and
find
A and B.
Solution: tan (A
+ B) = √3
⇒ tan (A + B) = tan 60°
⇒ A + B = 60° ………. (i)
tan
(A – B) = 1/√3
⇒ tan (A – B) = tan 30°
⇒ A – B = 30° ………. (ii)
Adding
equations (i) and (ii), we get
2A
= 90°
⇒ A = 45°
Putting
the value of A in equation (i), we get
45°
+ B = 60°
⇒ B = 15°
4. State whether the following 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 for A = 60° and B = 30°,
sin
(A + B) = sin (60° + 30°) = sin 90° = 1
And
sin A + sin B = sin 60° + sin 30° = √3/2 + ½ = (√3 + 1)/2
Therefore, sin (A + B) ≠ sin A + sin B
(ii) True, because
(iii) False, because
It
is clear, the value of cos θ decreases as θ increases.
(iv) False, since it is only true for θ =
45°.
⇒ sin 45° = 1/√2 = cos 45°
(v) True, because tan 0° = 0 and cot
0° = 1/tan 0°
= 1/0 i.e. undefined.