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(i) sin (A + B) = sin A + sin B.
(ii) The value of increases as
increases.
(iii) The value of increases as
increases.
(iv) for all values of
.
(v) cot A is not defined for A = .
Asked by Shreya Last Modified
Answer 
Tasneem
(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 90° = 1
Hence, the given statement is true.
(iii) cos 0° = 1
cos90° = 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 
It is not true for all other values of θ.
As 
and 
,
Hence, the given statement is false.
(v) cot A is not defined for A = 0°
As 
,
= undefined
Hence, the given statement is true.
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