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Statement I In a triangle ABC if tan A:...

Statement I In a triangle ABC if `tan A: tan B: tan C=1 :2:3, ` then `A=45^(@)`
Statement II If `p:q:r=1:2:3,` then `p=1`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement- 2 is True.

Text Solution

Verified by Experts

In a `!ABC`, we have tan A : tan B : tan C = 1 : 2: 3
So, let tan A= x, tan B = 2x and tan C = 3x.
We know that tan A + tan B + tan C = tan A tan B tan C
`rArrx+2x+3x=6x^(3)`
`rArrx=1[becausexne-1,0]`
`thereforetanA=1rArrA=45^(@)`
So, statement-1 is true.
Clearly, statement-2 is not true, because p : q: r = 1 : 2 : 3 for p = 3, q = 6 and r = 9, but p`ne1`.
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