(i) False.
Let A = 30° and B = 60°, then
sin (A + B) = sin (30° + 60°) = sin 90° = 1 and,
sin A + sin B = sin 30° + sin 60°
= 1/2 + √3/2 = 1+√3/2
(ii) True.
sin 0° = 0
sin 30° = 1/2
sin 45° = 1/√2
sin 60° = √3/2
sin 90° = 1
Thus the value of sin θ increases as θ increases.
(iii) False.
cos 0° = 1
cos 30° = √3/2
cos 45° = 1/√2
cos 60° = 1/2
cos 90° = 0
Thus the value of cos θ decreases as θ increases.
(iv) sin θ = cos θ for all values of θ.
This is true when θ = 45°
It is not true for all other values of θ.
Hence, the given statement is false.
(v) True.
cot A = cos A/sin A
cot 0° = cos 0°/sin 0° = 1/0 = undefined.
