Match the columnList IList IIA- cos 20-cos 80-3cos 50-1- -1B- cos 0-cos-7-cos2-7-cos3-7-cos4-7-cos5-7-cos6-72- -3-4C- cos 20-cos 40-cos 60-4cos 10-cos 20-cos 30-3- 1D- cos 20-cos 100-cos 100-cos 140-cos 140-cos 200-4- 0

The correct option is B A 4, B 3, C 1, D 2A) cos20+cos80 √( 3 ) cos50 =2cos( 20+80 2 #160;) cos( 20 80 2 #160;) √( 3 ) cos50 =2co ...

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Byju's Answer

Standard XII

Mathematics

Property 4

Match the col...

Question

Match the column
List I List II
A. $cos 20^{\circ} + cos 80^{\circ} - \sqrt{3} cos 50^{\circ}$ 1. $- 1$
B. $cos 0^{\circ} + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7}$ 2. $- \frac{3}{4}$
C. $cos 20^{\circ} + cos 40^{\circ} + cos 60^{\circ} + 4 cos 10^{\circ} cos 20^{\circ} cos 30^{\circ}$ 3. $1$
D. $cos 20^{\circ} cos 100^{\circ} + cos 100^{\circ} cos 140^{\circ} - cos 140^{\circ} cos 200^{\circ}$ 4. $0$

A- 4, B- 3, C- 1, D- 2

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A- 3, B- 4, C- 1, D- 2

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A- 4, B- 3, C- 2, D- 1

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A- 4, B- 1, C- 3, D- 2

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Solution

The correct option is B A- 4, B- 3, C- 1, D- 2
A) $c o s 20 + c o s 80 - \sqrt{3} c o s 50$
$= 2 c o s (\frac{20 + 80}{2}) c o s (\frac{20 - 80}{2}) - \sqrt{3} c o s 50 = 2 c o s 50 c o s 30 - \sqrt{3} c o s 50 = \sqrt{3} c o s 50 - \sqrt{3} c o s 50 = 0$
B) $c o s 0 + c o s \frac{π}{7} + c o s \frac{2 π}{7} + c o s \frac{3 π}{7} + c o s \frac{4 π}{7} + c o s \frac{5 π}{7} + c o s \frac{6 π}{7}$
$= 1 + c o s \frac{π}{7} + c o s \frac{2 π}{7} + c o s \frac{3 π}{7} + c o s (π - \frac{3 π}{7}) + c o s (π - \frac{2 π}{7}) + c o s (π - \frac{π}{7}) = 1 + c o s \frac{π}{7} + c o s \frac{2 π}{7} + c o s \frac{3 π}{7} - c o s \frac{3 π}{7} - c o s \frac{2 π}{7} - c o s \frac{π}{7} = 1$
C) $c o s 20 + c o s 40 + c o s 60 - 4 c o s 10 c o s 20 c o s 30$
$= 2 c o s 10 c o s 30 + c o s 60 - 2 (c o s 30 + c o s 10) c o s 30 = 2 c o s 10 c o s 30 + \frac{1}{2} - 2 {(\frac{\sqrt{3}}{2})}^{2} - 2 c o s 10 c o s 30 = \frac{1}{2} - \frac{3}{2} = - 1$
D) $c o s 20 c o s 100 + c o s 100 c o s 140 - c o s 140 c o s 200$
$= \frac{1}{2} (c o s 120 + c o s 80) + \frac{1}{2} (c o s 240 + c o s 40) - \frac{1}{2} (c o s 340 + c o s 60) = \frac{1}{2} (- s i n 30 + c o s 80 - c o s 60 + c o s 40 - c o s 20 - c o s 60) = \frac{1}{2} (- \frac{3}{2} + (c o s 40 + c o s 80) - c o s 20) = \frac{1}{2} (- \frac{3}{2} + 2 c o s 60 c o s 20 - c o s 20) = - \frac{3}{4}$

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Similar questions

If
A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {6, 7, 8, 9}

D = {7, 8, 9, 10}

$\begin{matrix} C o l u m n A & C o l u m n B 1. A \cup B & a . {3, 4, 6, 7} 2. A \cap B & b . \emptyset 3. (B \cap C) \cup D & c . {3, 4} 4. B \cup C \cup D & d . {3, 4, 5, 6, 7, 8, 9, 10} 5. (A \cap B) \cap (B \cup C) & e . {1, 2, 3, 4, 5, 6, 7} f . {6, 7, 8, 9, 10} g . {7} \end{matrix}$

Q. Evaluate:

cos 20^{\circ} cos 100^{\circ} + cos 100^{\circ} cos 140^{\circ} - cos 140^{\circ} cos 200^{\circ}

cos 20^{\circ} cos 100^{\circ} + cos 100^{\circ} cos 140^{\circ} - cos 140^{\circ} . cos 200^{\circ}

is equal to

Simplify:

(a)

\frac{2}{3} + \frac{1}{7}

(b)

\frac{3}{10} + \frac{7}{15}

(c)

\frac{4}{9} + \frac{2}{7}

(d)

\frac{5}{7} + \frac{1}{3}

(e)

\frac{4}{5} + \frac{2}{3}

(f)

\frac{3}{4} - \frac{1}{3}

(g)

\frac{5}{6} - \frac{1}{3}

Q. The value of the expression

cos 20^{\circ} cos 100^{\circ} + cos 100^{\circ} cos 140^{\circ} - cos 140^{\circ} cos 200^{\circ}

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	List I		List II
A.	$cos 20^{\circ} + cos 80^{\circ} - \sqrt{3} cos 50^{\circ}$	1.	$- 1$
B.	$cos 0^{\circ} + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7}$	2.	$- \frac{3}{4}$
C.	$cos 20^{\circ} + cos 40^{\circ} + cos 60^{\circ} + 4 cos 10^{\circ} cos 20^{\circ} cos 30^{\circ}$	3.	$1$
D.	$cos 20^{\circ} cos 100^{\circ} + cos 100^{\circ} cos 140^{\circ} - cos 140^{\circ} cos 200^{\circ}$	4.	$0$

Match the columnList IList IIA.cos20∘+cos80∘−√3cos50∘1.−1B.cos0∘+cosπ7+cos2π7+cos3π7+cos4π7+cos5π7+cos6π72.−34C.cos20∘+cos40∘+cos60∘+4cos10∘cos20∘cos30∘3.1D.cos20∘cos100∘+cos100∘cos140∘−cos140∘cos200∘4.0