What is the value of Cos0 x cos1 x cos2 x...........x cos89 = ?
Saptarshi Kar , 7 Years ago
Grade 12th pass
Trigonometry> What is the value of Cos0 x cos1 x cos2 x...
2 Answers
Arun
Last Activity: 7 Years ago
Dear student
In between there will be a cos 90 degree too
hence
cos 90 = 0
now if 0 is multiplied in any number answer will be 0
Hence value of your question will be 0.
Regards
Arun (askIITians forum expert)
Arun
Last Activity: 7 Years ago
Dear student
Sorry I got your question in wrong way.
Actual solution is as follows β
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
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available
Last Activity: 3 Years ago
- Find the general solution of equation tan3β=cot2β
For all angles between -720 and +720
- Find the general solution of equation tan3β=cot2β
For all angles between -720 and +720
trigonometry
1 Answer Available
Last Activity: 3 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available
Last Activity: 3 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available
Last Activity: 3 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? limπ₯β0 π ππ6π₯/5π₯
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? limπ₯β0 π ππ6π₯/5π₯
trigonometry
1 Answer Available
Last Activity: 3 Years ago