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Question

If in a right-angled triangle ABC angles A and B are acute, then evaluate

1 + tanAtanB =


A

1

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B

sec2A

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C

secA

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D

2

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Solution

The correct option is B

sec2A


Given, in a right-angled triangle ABC angles A and B are acute.
Hence, A + B = 90.

So, 1 + tan(90°B)tanB ...[tan(90θ)=cotθ]

= 1 + cotBtanB
We know 1tanB=cotB

= 1 + cot2B

= 1 + cot2(90°A)

= 1 + tan2A

= sec2A (sec2Atan2A=1)


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