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Find the value of tan A, if area of Delt...

Find the value of tan A, if area of `Delta ABC is a^(2) -(b-c)^(2).`

A

`(4)/(15)`

B

`(8)/(15)`

C

`(11)/(15)`

D

`(13)/(15)`

Text Solution

Verified by Experts

The correct Answer is:
B
If `Delta = a^(2)-(b-c)^(2)` …………
`Delta = a^(2)-(b-c)^(2)implies b^(2)+c^(2)-a^(2)=2bc-Delta`
`2bc cos A = 2bc-Delta ( :' cos A = (b^(2)+c^(2)-a^(2))/(2bc))`
`= 2bc - (1)/(2) bc sin A`
`implies 4 cos A + sin A = 4 implies tan (A)/(2) = (1)/(4) :. tan A = (8)/(15)`
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