Question

# Question 6 The value of (tan1∘,tan2∘,tan3∘……tan89∘) is (A) 0 (B) 1 (C) 2 (D) 12

Solution

## The answer is (B). Thinking Process Use the transformation tan(90∘−θ)=cotθ  from greater than trigonometric angle tan45∘ after that we use the trigonometric ratio, cotθ=1tanθ tan1∘,tan2∘,tan3∘……tan89∘ =tan1∘,tan2∘,tan3∘……tan44∘,tan45∘,tan46∘……tan87∘,tan88∘,tan89∘ =tan1∘,tan2∘,tan3∘……tan44∘,(1).tan(90∘−44∘)……tan(90∘−3∘)tan(90∘−2∘).tan(90∘−1∘)   (∵tan45∘=1) =tan1∘,tan2∘,tan3∘……tan44∘,(1).cot44∘……cot3∘.cot2∘,cot1∘ ⌊∵tan(90−θ)=cotθ⌋ (\because tan 45^{\circ}=1)z\) =tan1∘,tan2∘,tan3∘……tan44∘,(1)…1tan44∘…1tan30∘…1tan1∘[∵cotθ=1tanθ]

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