Question

a + b + c = π and cos A = cos B cos C then tan B . tan C has the value equal to

A) 1

B) 1/2

C) 2

D) 3
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plz solve

10 marks

Answer 1

Answer:

Option (C)

Explanation:

Given cosA = cosB * cosC  ------- (1)

$= \ \textgreater \ Given: A + B + C = \pi$

$= \ \textgreater \ B + C = \pi - A$

Apply cos on both sides, we get

$= \ \textgreater \ cos(B + C) = cos( \pi - A)$

We know that Cos(A + B) = cosAcosB - sinAsinB and cos(180 - A) = -cosA.

= > cosBcosC - sinBsinC = -cosA

= > cosBcosC - sinBsinC = -cosBcosC(From (1))

= > cosBcosC - sinBsinC + cosBcosC = 0

= > 2cosBcosC = sinBsinC

= > 2 = sinBsinC/cosBcosC.


Now,

We know that TanA = sinA/cosA.

Therefore TanBTanC = sinAsinB/cosBcosC

                                    = 2.



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks