(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°.
NCERT Class 10 Chapter 8 Introduction to Trigonometry
Page No. 187
Exercise 8.2
Question No. 4
(i) False,
Let A = 30° and B = 60°
Therefore, LHS = sin(A + B) = sin(30° + 60°) = sin 90° 1 and
RHS = sin A + sin B = sin 30° + sin 60° = 1/2 + √3/2 = (1+√3)/2 ≠ 1
Hence, sin (A + B) ≠ sin A + sin B
(ii) True,
As we know that sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2 and sin 90° = 1
Hence, for the increasing values of θ, sin θ is also increasing.
(iii) False,
As we know that cos 0° = 1, cos 30° = √3/2, cos 45° = 1√2, cos 60° = 1/2 and cos 90° = 0
Hence, for the increasing values of θ, cos θ is decreasing.
(iv) False,
∵ cos 30° = √3/2, but sin 30° = 1/2.
(v) True,
∵ tan 0° = 0, we know that cot 0° = 1/tan 0° = 1/0, which is not defined.
See the explanation video of the above solution here✌