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Question

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

1 + tanAtanB =


  1. 1

  2.  secA

  3.  sec2A

  4. 2


Solution

The correct option is C

 sec2A


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

So, 1 + tan(90B)tanB

=  1 + cotBtanB
We know 1tanB=cotB

= 1 + cot2B 

= 1 +  cot2(90A)

= 1 + tan2A

 = sec2A           (sec2Atan2A=1)

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