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°
(i) sin (A + B) = sin A + sin B
Let A = 30° and B = 60°
sin (A + B) = sin (30° + 60°)
= sin 90°
= 1
sin A + sin B = sin 30° + sin 60°
= 
= 
Clearly, sin (A + B) ≠sin A + sin B
Hence, the given statement is false
(ii) The value of sin θ increases as θ increases in the interval of 0° < θ < 90° as sin 0° = 0
sin 30o = 
sin 45o = 
= 0.707
sin 60o = 
= 0.886
sin 90° = 1
Hence, the given statement is true
(iii) cos 0° = 1
cos 30o = 
cos 45o = 
cos 60o = 
cos 90° = 0
It can be observed that the value of cos θ does not increase in the interval of 0° < θ < 90°
Hence, the given statement is false
(iv) sin θ = cos θ for all values of θ.
This is true when θ = 45°
As,
sin 45o = 
cos 45o = 
It is not true for all other values of θ
As sin 30o = 
and cos 30o = 
Hence, the given statement is false
(v) cot A is not defined for A = 0°
cot A = 
cot 0o = 
= 
=undefined
Hence, the given statement is true