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Question

Question 6
The value of
(tan1,tan2,tan3tan89) is

(A) 0
(B) 1
(C) 2
(D) 12


Solution

The answer is (B).

Thinking Process
Use the transformation tan(90θ)=cotθ  from greater than trigonometric angle tan45 after that we use the trigonometric ratio, cotθ=1tanθ

tan1,tan2,tan3tan89

=tan1,tan2,tan3tan44,tan45,tan46tan87,tan88,tan89

=tan1,tan2,tan3tan44,(1).tan(9044)tan(903)tan(902).tan(901)   (tan45=1)

=tan1,tan2,tan3tan44,(1).cot44cot3.cot2,cot1

tan(90θ)=cotθ

(\because tan 45^{\circ}=1)z\)

=tan1,tan2,tan3tan44,(1)1tan441tan301tan1[cotθ=1tanθ]
 

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