State whether the following are true or false. Justify your answer.
(i) sin(A+B)=sinA+sinB
(ii) The value of sinθ increases as θ increases.
(iii) The value of cosθ increases as θ increases.
(iv) sinθ=cosθ for all values of θ.
(v) cotA is not defined for A=0°

(i) False
sin(A+B)=sinA+sinB
A=45°, B=45°
LHS: sin(45°+45°)=sin90°=1
RHS : sinA+sinB=1/√2+1/√2=2/√2=√2
LHS≠RHS
(ii) True
sin0°=0
sin30°=1/2
sin45°=1/√2,
sin60°=√3/2
sin90°=1
∴ θ increase and value of sinθ also increase
(iii) False
cos0=1, cos30=√3/2, cos45=1/√2
cos60=1/2, cos90=0
Value of cosθ does not increase from 0<θ<90°
(iv) False
This is true for θ=45°
Let θ=90°
sin90=1, cos90=0
(v) True
cotA=cosA/sinA
cot0°=cos0/sin0=1/0=not defined