In a - ABC - the value of cos 2 B - C -2- b - c 2-sin 2 B - C -2- b - c 2 isA- a2B- b 2- c 2- a 2C- b22-c2-1a2D- 1 a 2- a 2

The correct option is D 1/a^2cos^2B C/2/4R^2. 4sin^2 B+C/2. cos^2B C/2+sin^2B C/2/4R^2. 4cos^2 B+C/2. sin^2B C/2 =1/16R^2 [ 1/cos^2A/2+1/sin^2A/2 ]=1/4.R. ( 2 ...

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Standard X

Mathematics

Complementary Trigonometric Ratios

In a Δ ABC ; ...

Question

In a $Δ A B C$ ; the value of $\frac{c o s^{2} \frac{B - C}{2}}{(b + c)^{2}} + \frac{s i n^{2} \frac{B - C}{2}}{(b - c)^{2}}$ is

a^{2}

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\frac{1}{a^{2}}

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

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

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Solution

The correct option is B $\frac{1}{a^{2}}$
$\frac{c o s^{2} \frac{B - C}{2}}{4 R^{2} . 4 s i n^{2} \frac{B + C}{2} . c o s^{2} \frac{B - C}{2}} + \frac{s i n^{2} \frac{B - C}{2}}{4 R^{2} . 4 c o s^{2} \frac{B + C}{2} . s i n^{2} \frac{B - C}{2}} = \frac{1}{16 R^{2}} [\frac{1}{c o s^{2} \frac{A}{2}} + \frac{1}{s i n^{2} \frac{A}{2}}] = \frac{1}{4. R . {(2 s i n \frac{A}{2} . c o s \frac{A}{2})}^{2}} = \frac{1}{4 R^{2} s i n^{2} A} = \frac{1}{a^{2}}$

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Similar questions

Q. In a

Δ A B C

; the value of

\frac{c o s^{2} \frac{B - C}{2}}{(b + c)^{2}} + \frac{s i n^{2} \frac{B - C}{2}}{(b - c)^{2}}

Q. In a

Δ A B C

; the value of

\frac{c o s^{2} \frac{B - C}{2}}{(b + c)^{2}} + \frac{s i n^{2} \frac{B - C}{2}}{(b - c)^{2}}

Mark the correct alternative in each of the following :

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

Prove that :

\frac{{cos}^{2} \frac{B - C}{2}}{(b + c)^{2}} + \frac{{sin}^{2} \frac{B - C}{2}}{(b - c)^{2}} = \frac{1}{a^{2}}

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}

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In a ΔABC; the value of cos2B−C2(b+c)2+sin2B−C2(b−c)2 is

The correct option is B 1a2cos2B−C24R2.4sin2B+C2.cos2B−C2+sin2B−C24R2.4cos2B+C2.sin2B−C2=116R2[1cos2A2+1sin2A2]=14.R.(2sinA2.cosA2)2 =14R2sin2A=1a2

In a $Δ A B C$ ; the value of $\frac{c o s^{2} \frac{B - C}{2}}{(b + c)^{2}} + \frac{s i n^{2} \frac{B - C}{2}}{(b - c)^{2}}$ is