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4. 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°.

4. 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°.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8740 Points
3 months ago
(i) False. Justification: Let us take A = 30° and B = 60°, then Substitute the values in the sin (A + B) formula, we get sin (A + B) = sin (30° + 60°) = sin 90° = 1 and, sin A + sin B = sin 30° + sin 60° = 1/2 + √3/2 = 1+√3/2 Since the values obtained are not equal, the solution is false. (ii) True. Justification: According to the values obtained as per the unit circle, the values of sin are: 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. Hence, the statement is true (iii) False. According to the values obtained as per the unit circle, the values of cos are: 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. So, the statement given above is false. (iv) False sin θ = cos θ, when a right triangle has 2 angles of (π/4). Therefore, the above statement is false. (v) True. Since cot function is the reciprocal of the tan function, it is also written as: cot A = cos A/sin A Now substitute A = 0° cot 0° = cos 0°/sin 0° = 1/0 = undefined. Hence, it is true

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