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u r right but in the question they did not gave total information

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Comment has been deleted

u r right but in the question they did not gave total information

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In a triangle : angle A =2 * angle C

so angle B = 180 deg - 2 angle C - angle C

B = 180 - 3 C

we know that

Sin 2C = 2 Sin C Cos C

Sin 3C = 3 Sin C - 4 Sin³ C = Sin C [ 3 - 4 Sin² C ] = Sin C [ 2 Cos 2C + 1 ]

we know that:*a / Sin A = b / Sin B = c / Sin C*

=> a / Sin 2C = b / Sin 3C = c / Sin C

=>* a = 2 c Cos C * -- (1)

and*b** = c {1 + 2 Cos 2C ] * --- (2)

Now find a² - c² = 4 c² Cos² C - c²

= c² [ 4 Cos² C - 1 ]

= c² [ 2 Cos 2C + 1 ]

substitute from (2),

a² - c² =c² * b/c = bc

=>* a² = c (b+c)*

proved.

so angle B = 180 deg - 2 angle C - angle C

B = 180 - 3 C

we know that

Sin 2C = 2 Sin C Cos C

Sin 3C = 3 Sin C - 4 Sin³ C = Sin C [ 3 - 4 Sin² C ] = Sin C [ 2 Cos 2C + 1 ]

we know that:

=> a / Sin 2C = b / Sin 3C = c / Sin C

=>

and

Now find a² - c² = 4 c² Cos² C - c²

= c² [ 4 Cos² C - 1 ]

= c² [ 2 Cos 2C + 1 ]

substitute from (2),

a² - c² =c² * b/c = bc

=>

proved.