(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°.
State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B.
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Solution:
(i) It is not true, in general. This relation is true for some particular values of A and B.
For example, if A = 0 and B = 90,
Then, Sin (A+B) = sin (0+90) = sin 90 = 1
And, sin A + sin B = sin 0 + sin 90 = 0 + 1 = 1
Hence, sin (A+B) = sin A + sin B
(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) True.
cot A = cos A/sin A
cot 0° = cos 0°/sin 0° = 1/0 = undefined
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