Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

# If the sides of a ∆ABC are a = 4, b = 6 and c = 8, then show that 4 cos B + 3 cos C = 2 - Mathematics

Sum

If the sides of a ∆ABC are a = 4, b = 6 and c = 8, then show that 4 cos B + 3 cos C = 2

#### Solution

a = 4,

b = 6,

c = 8

To prove 4 cos B + 3 cos C = 2

cos B = ("a"^2 + "c"^2 - "b"^2)/(2"ac")

= (16 + 64 - 36)/(2(4)(8))

= (80 - 36)/64

= 44/64

= 11/16

cos C = ("a"^2 + "b"^2 - "c"^2)/(2"ab")

= (16 + 36 - 64)/(2(4)(6))

= (-12)/48

= - 1/4

So L.H.S = 4 cos B + 3 cos C

= 4(11/16) + 3(- 1/4)

= 11/4 - 3/4

= 8/4

= 2

= R.H.S

Concept: Application to Triangle
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