Question

In a ΔABC, c² sin 2B + b² sin 2C = ?

Options

• Δ

• 2Δ

• 3Δ

• 4Δ

Answer 1

4Δ

Explanation:

c² sin 2B + b² sin 2C

= c²(2 sin B cos B) + b²(2 sin C cos C)

Since Δ = `1/2` ac sin B = `1/2` ab sin C

∴ sin B = `(2Δ)/"ac", sin "C" = (2Δ)/"ab"`

∴  c² sin 2B + b² sin 2C

`= 2"c"^2 ((2Δ)/"ac" cos "B") + 2"b"^2 ((2Δ)/"ab" cos "C")`

`= 4Δ ((c cos "B" + "b" cos "C")/"a")`

= 4Δ`("a"/"a")`    .....[by projection rule]

= 4Δ