Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
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
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !