AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Match the items of List I with items of List II and choose the correct option.
Column-I Column-II
A) $\cos 20^{0} + \cos 80^{0} - \sqrt{3} \cos 50^{0}$ P)-1
B) $\cos 0^{0} + \cos \frac{π}{7} + \cos \frac{2 π}{7} + \cos \frac{3 π}{7} + \cos \frac{4 π}{7} + \cos \frac{5 π}{7} + \cos \frac{6 π}{7}$ q) $- \frac{3}{4}$
C) $\cos 20^{0} + \cos 40^{0} + \cos 60^{0} - 4 \cos 10^{0} \cos 20^{0} \cos 30^{0}$ r) 1
D) $\cos 20^{0} \cos 100^{0} + \cos 100^{0} \cos 140^{0} - \cos 140^{0} \cos 200^{0}$ s) 0

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$B \to r A \to s D \to q C \to p$

$C \to p B \to r D \to q A \to s$

$A \to s, B \to r, C \to p, D \to q$

$D \to r A \to s C \to p B \to r$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

A) $\begin{aligned} = 2 \cos 50 ° \cos 30 ° - \sqrt{3} \cos 50 ° \\ = 2 \cdot \frac{\sqrt{3}}{2} \cos 50 ° - \sqrt{3} \cos 50 ° = 0 \end{aligned}$

B) $\begin{aligned} = \cos 0 ° + \cos \frac{π}{7} + \cos \frac{2 π}{7} + \cos \frac{3 π}{7} + \cos \frac{4 π}{7} + \cos \frac{5 π}{7} + \cos \frac{6 π}{7} \\ = \cos 0 ° + \cos \frac{π}{7} + \cos \frac{2 π}{7} \cdot \cos \frac{3 π}{7} + \cos (π - \frac{3 π}{7}) + \cos (π - \frac{2 π}{7}) \\ + \cos (π - \frac{π}{7}) \\ = 1 + \cos \frac{π}{7} + \cos \frac{2 π}{7} + \cos \frac{3 π}{7} - \cos \frac{3 π}{7} - \cos \frac{2 π}{7} - \cos \frac{π}{7} = 1 \end{aligned}$

C) $\cos 20 ° + \cos 40 ° + \cos 60 ° - 4 (\cos 10 ° \cos 20 ° \cos 30 ° = \cos 20 ° + \cos 40 ° + \cos 60 ° - 2 (2 \cos 10 ° \cos 20) \cos 30 = 2 \cos 30 ° \cos 10 ° + \frac{1}{2} - 2 (\cos 30 ° + \cos 10 °) \frac{\sqrt{3}}{2} = 2 \frac{\sqrt{3}}{2} \cos 10 ° + \frac{1}{2} - 2 {(\frac{\sqrt{3}}{2})}^{2} - 2 \cos 10 ° (\frac{\sqrt{3}}{2}) = \frac{1}{2} - \frac{3}{2} = - 1$

D) $\cos 20^{0} \cos 100^{0} + \cos 100^{0} \cos 140^{0} - \cos 140^{0} \cos 200^{0} = = \frac{\cos 120 ° + \cos 80 °}{2} + \frac{\cos 240^{\circ} + \cos 40 °}{2} - \frac{\cos 340 ° + \cos 60 °}{2}$

$= \frac{1}{2} [- \frac{1}{2} + \cos 80 ° - \frac{1}{2} + \cos 40 ° - \cos 340 ° - \frac{1}{2}] = \frac{1}{2} [- \frac{3}{2} (\cos 80 ° + \cos 40 °) - \cos 340] = \frac{- 3}{4} + \frac{1}{2} (2 \cos 60 ° \cos 20 ° - \cos 20 °) = \frac{- 3}{4}$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!