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Mathematics : Introduction to Trigonometry

Short Answer Type

11. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = 12/5 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ= 4/3 for some angle 6.

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12. Evaluate:
sin 60° cos 30° + sin 30° cos 60°

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13. Evaluate:
2 tan² 45° + cos² 30° - sin² 60°

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14. Evaluate:

fraction numerator cos space 45 degree over denominator sec space 30 degree space plus space cosec space 30 degree end fraction.

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15. Choose the correct option and justify your choice:

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(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°.

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16.

Choose the correct option and justify your choice:
$fraction numerator 1 minus tan squared 45 degree over denominator 1 plus tan squared 45 degree end fraction$

(A) tan 90° (B) 1 (C) sin 45° (D) 0.

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17.

Choose the correct option and justify your choice:
sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°

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18.

Choose the correct option and justify your choice:
$fraction numerator 2 tan 30 degree over denominator 1 minus tan squared 30 degree end fraction equals$
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°.

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19.

If $tan left parenthesis straight A plus straight B right parenthesis space equals square root of 3 space space and space tan left parenthesis straight A minus straight B right parenthesis space equals space fraction numerator 1 over denominator square root of 3 end fraction semicolon$ $0 degree less than straight A plus straight B less or equal than 90 degree semicolon space space space straight A greater than straight B.$ Find A and B.

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20. State whether the following are true false. Justify your answer.
sin (A + B) = sin A + sin B.

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