# 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° NCERT Class X Mathematics - Mathematics Chapter _INTRODUCTION TO TRIGONOMETRY

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by jayGola97

2015-06-12T08:40:55+05:30
(i) sin (A + B) = sin A + sin B.
It is false
sin (A + B) = sin A cos B + sin B cos A

(ii) The value of sin θ increases as θ increases.
It is false. It is a periodic function with period 2π. It increases from 0 to π/2, then decreases till 3π/2 and then increases till 2π.

(iii) The value of cos θ increases as θ increases.
It is false. It is a periodic function with period 2π. decreases from 0 to π and then increases till 2π.

(iv) sin θ = cos θ for all values of θ.
It is false. The instances when it is true is θ = (nπ + π/4) where n = 0,1,2,3...

(v) cot A is not defined for A = 0°
It is true. We take cot 0 to be ∞ which is not defined.