Question

if in a triangle ABC a=7,b=5,c=8 then find the value of cos2A. ?

Answer 1

According to the question we need here the formula of CosA

from Cosine rules we know that

$cos \: a = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc}$

now, put the above values

$= \frac{25 + 64 - 49}{2 \times 5 \times 8} \\ = \frac{1}{2}$

Then cos2A = 2cos²A-1

$= 2 \times \frac{1}{4} - 1$

$= - \frac {1}{2}$

Answer 2

$cos \: a = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc}$

now,

$= \frac{25 + 64 - 49}{2 \times 5 \times 8} \\ = \frac{1}{2}$

we know that cos2A = 2cos²A-1

$= 2 \times \frac{1}{4} - 1$

$= - \frac {1}{2}$