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If alpha+beta=pi/2 and beta+gamma=alpha ...

If `alpha+beta=pi/2` and `beta+gamma=alpha` then `tanalpha` equals

A

`2(tanbeta+tangamma)`

B

`tanbeta+tangamma`

C

`tan beta+2 tangamma`

D

`2tanbeta+tangamma`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`beta+gamma+alpha`
`impliesgamma=alpha=beta`
`tangamma=tan(alpha-beta)`
`impliestangamma=(tanalpha-tanbeta)/(1+tanalphatanbeta)`
`impliestangamma=(tanalpha-tanbeta)/(1+tanalphacot alpha)" "[becausealpha+beta=(pi)/(2)becausebeta=(pi)/(2)-alpha]`
`impliestangamma=1/2(tangamma-tanbeta)impliestanalpha=tanbeta+2tangamma.`
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