In - ABC - - C -2 -3- then the value of cos 2 A -cos 2 B -cos A -cos B -A- 1-4B- -3-12C- D- 3-4

The correct option is D 3/4 ∠ C =2π/3∴ A+B =π/3 Now cos^2 A +cos^2 B cos A cos B =1+cos 2A/2+1+cos 2 B/2 1/2[cos (A+B)+cos(A B)] =1/2[2+2 cos (A+B)cos (A B)] 1 ...

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Byju's Answer

Standard XI

Mathematics

Equations of the form acos?+bsin? = c

In Δ ABC , ∠ ...

Question

In $Δ A B C, ∠ C = \frac{2 π}{3}$ , then the value of $c o s^{2} A + c o s^{2} B - c o s A . c o s B =$ ___

$\frac{1}{2}$

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$\frac{1}{4}$

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$\frac{3}{4}$

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$\frac{\sqrt{3}}{2}$

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Solution

The correct option is C
$\frac{3}{4}$

$∠ C = 2 \frac{π}{3} ∴ A + B = \frac{π}{3}$
Now $c o s^{2} A + c o s^{2} B - c o s A c o s B = \frac{1 + c o s 2 A}{2} + \frac{1 + c o s 2 B}{2} - \frac{1}{2} [c o s (A + B) + c o s (A - B)]$
$= \frac{1}{2} [2 + 2 c o s (A + B) c o s (A - B)] - \frac{1}{2} [\frac{1}{2} + c o s (A - B)] = \frac{1}{2} [2 + 2 \frac{1}{2} c o s (A - B)] - \frac{1}{4} - \frac{1}{2} c o s (A - B) = 1 - \frac{1}{4} = \frac{3}{4}$

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Similar questions

In $Δ A B C, ∠ C = \frac{2 π}{3}$ , then the value of $c o s^{2} A + c o s^{2} B - c o s A . c o s B =$ ___

Q. In

Δ A B C, ∠ C = 90^{\circ}

, then the value of

{cos}^{2} A + {cos}^{2} B

is :

Q. In

Δ A B C

prove:

cos 2 A + cos 2 B + cos 2 C = - 1 - 4 cos A cos B cos C

Q. Assertion :If

A + B + C = π

then Statement 1:

{cos}^{2} A + {cos}^{2} B + {cos}^{2} C

has its minimum value

\frac{3}{4}

Reason: Statement 2: Maximum value of

cos A cos B cos C

\frac{1}{8}

If A + B + C = $π$ . Then

$\begin{matrix} Column A & Column B 1.sin2A + sin2B + sin2C & A.cos \frac{A}{2} cos \frac{B}{2} cos \frac{C}{2} 2.sinA + sinB + sinC & B.1+4sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2} 3.cos2A + cos2B + cos2C & C.4sinA sinB sinC 4.cosA + cosB + cosC & D.-1-4cosA + cosB + cosC \end{matrix}$

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In ΔABC,∠C=2π3, then the value of cos2A+cos2B−cosA.cosB=___

The correct option is C 34 ∠C=2π3∴A+B=π3 Now cos2A+cos2B−cosAcosB=1+cos2A2+1+cos2B2−12[cos(A+B)+cos(A−B)] =12[2+2cos(A+B)cos(A−B)]−12[12+cos(A−B)]=12[2+212cos(A−B)]−14−12cos(A−B)=1−14=34

In $Δ A B C, ∠ C = \frac{2 π}{3}$ , then the value of $c o s^{2} A + c o s^{2} B - c o s A . c o s B =$ ___