Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
What is the value of Cos0 x cos1 x cos2........................x cos89
Let Us Divide The Question Into Two PartsFirst Let Us Solve For Cosine Seriescos1. cos2. cos3 ..... cos89Let Us Club The First And Last Terms,then second and second last and so on(cos1. cos89) (cos2. cos88) (cos3 .cos87) .... (cos44. cos46) cos45cos45 will remain as no pairing will occurNowcos(90-x) = sinxApplying The Above formula In the series(cos1. sin1) (cos2. sin2) .... (cos44.sin44). cos45Similarly Doing For Sine Series(sin1. sin89) (sin2. sin88) (sin3. sin87) .... (sin44. sin46). sin45Applying sin(90-x) = cosx(sin1. cos1) (sin2. cos2) (sin3. cos3) .... (sin44. cos44). sin45Now We Know That Sin45 = Cos45So The Final Sine Series Becomes(cos1.sin1) (cos2.sin2) (cos3.sin3) .... (cos44. sin44). cos45 Which is exactly the same as cosine seriesThey are exactly same seriesso if we subtraction themAnswer= Zero
Let Us Divide The Question Into Two Parts
First Let Us Solve For Cosine Series
cos1. cos2. cos3 ..... cos89
Let Us Club The First And Last Terms,then second and second last and so on
(cos1. cos89) (cos2. cos88) (cos3 .cos87) .... (cos44. cos46) cos45
cos45 will remain as no pairing will occur
Now
cos(90-x) = sinx
Applying The Above formula In the series
(cos1. sin1) (cos2. sin2) .... (cos44.sin44). cos45
Similarly Doing For Sine Series
(sin1. sin89) (sin2. sin88) (sin3. sin87) .... (sin44. sin46). sin45
Applying sin(90-x) = cosx
(sin1. cos1) (sin2. cos2) (sin3. cos3) .... (sin44. cos44). sin45
Now We Know That Sin45 = Cos45
So The Final Sine Series Becomes
(cos1.sin1) (cos2.sin2) (cos3.sin3) .... (cos44. sin44). cos45
Which is exactly the same as cosine series
They are exactly same series
so if we subtraction them
Answer= Zero
Find solution of question on doubt solving app Instasolv
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -