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Evaluate:!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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i) tan1°.tan2°ͦ.tan3°............…‡tan89°

ii) sin 30° cos60° cosec 30° sec 60°.

iii) tan2 60° +4 cos24?

asked May 27, 2013 in TRIGONOMETRY by anonymous Apprentice

3 Answers

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i)

  tan1º×tan2º×tan3º-----------tan45º------------tan89º

  =tan1º×tan2º×tan3º-----------tan45º------------tan87º×tan88º×tan89º

 =tan1º×tan2º×tan3º-----------tan45º------------tan(90 - 3)º×tan(90 - 2)º×tan(90 - 1)º

Recall : Trigonometry identities tan(90 - x) = cotx where x = 1º×2º×3º×4º----------45º

=tan1º×tan2º×tan3º-----------tan45º------------cot3º×cot2º×cot1º

=tan1º×cot1º×tan2º×cot2º×tan3º×cot3º-----------tan45º

Recall : Trigonometry tables tan45º = 1

=1×1×1×1-----------1

=1.

answered May 27, 2013 by diane Scholar
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ii)

    sin30º×cos60º×csc30º×sec60º

Recall : Trigonometry tables sin30º = cos60º = 1 / 2 and csc30º = sec60º = 2

Substitute the values sin30º = cos60º = 1 / 2 and csc30º = sec60º = 2 in the above function

 =1 / 2 ×1 / 2×2×2

=1 ×1

=1.

 

 

answered May 27, 2013 by diane Scholar
0 votes

iii)  The trigonometric expression is  image

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answered Jul 26, 2014 by david Expert

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