Mark the correct alternative in each of the following In any - ABC- the value of 2 ac sin A - B - C -2 isA- a2-b2-c2B- b2-c2-a2C- c2-a2-b2D- c 2- a 2- b 2

The correct option is D c^2+a^2 b^2 In Δ ABC A+B+C/2 B=π/2 B ⇒ A+C B/2=π/2 B ∴ 2ac sin 1/2(A B+C )=2ac sin (π/2 B ) =2ac cos B=2ac.a^2+c^2 b^2/2ac =a^2+c^2 ...

329

You visited us 329 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Cosine Rule

Mark the corr...

Question

Mark the correct alternative in each of the following :

$I n a n y Δ A B C, the value of 2ac s i n (\frac{A - B + C}{2}) i s$

$a^{2} + b^{2} - c^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$c^{2} + a^{2} - b^{2}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$b^{2} - c^{2} - a^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$c^{2} - a^{2} - b^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$c^{2} + a^{2} - b^{2}$

$I n Δ A B C \frac{A + B + C}{2} - B = \frac{π}{2} - B \Rightarrow \frac{A + C - B}{2} = \frac{π}{2} - B ∴ 2 a c s i n \frac{1}{2} (A - B + C) = 2 a c s i n (\frac{π}{2} - B) = 2 a c c o s B = 2 a c . \frac{a^{2} + c^{2} - b^{2}}{2 a c} = a^{2} + c^{2} - b^{2}$

Suggest Corrections

Similar questions

Q. Mark the correct alternative in each of the following:

In any ∆ABC, the value of

2 a c \sin (\frac{A - B + C}{2})

is

(a)

a^{2} + b^{2} - c^{2}

(b)

c^{2} + a^{2} - b^{2}

(c)

b^{2} - c^{2} - a^{2}

(d)

c^{2} - a^{2} - b^{2}

Q. Mark the correct alternative in each of the following:

In any ∆ABC,

\sum_{}^{} a^{2} (\sin B - \sin C) =

(a)

a^{2} + b^{2} + c^{2}

(b)

a^{2}

(c)

b^{2}

(d) 0

Mark the correct alternative in each of the following :

$I n a n y Δ A B C, 2 (b c c o s A + c a c o s B + a b c o s C) =$

Q. In

△ A B C, \frac{s i n (A - B)}{s i n (A + B)} =

[MP PET 1986]

In a $△ A B C, 2 c a s i n (\frac{A - B + C}{2})$ is equal to

Join BYJU'S Learning Program

Mark the correct alternative in each of the following : In any ΔABC, the value of 2ac sin(A−B+C2) is

The correct option is B c2+a2−b2 In ΔABCA+B+C2−B=π2−B⇒ A+C−B2=π2−B∴ 2ac sin 12(A−B+C)=2ac sin(π2−B)=2ac cos B=2ac.a2+c2−b22ac=a2+c2−b2

Mark the correct alternative in each of the following :

$I n a n y Δ A B C, the value of 2ac s i n (\frac{A - B + C}{2}) i s$