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(1+tanalphatanbeta)^2+(tanalpha-tanbeta)...

`(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=`

A

`tan^2alphatan^2beta`

B

`sec^2alphasec^2beta`

C

`tan^2alphacot^2beta`

D

`sec^2alphacos^2beta`

Text Solution

Verified by Experts

The correct Answer is:
B
`(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2`
`=1+2tanalphatanbeta+tan^2alphatan^2beta+tan^2alpha+tan^2beta-2tanlphatanbeta`
`=1tan^2alphatan^2beta+tan^2alpha+tan^2beta`
`+(1+tan^2alpha)(1+tan^2beta)`
`=sec^2alphasec^2beta`
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