Question

46. Find the value of cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (360°)​

Answer 1

Answer:

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CBSE

Mathematics

Grade 11

Trigonometric Ratios

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Related Questions

The value of cos10cos20cos30...cos900...cos1790

is?

A.12–√

B.0

C.1

D.None of these

Answer

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Hint: First, we will rewrite the given values and then use the cosine value cos90=0

, in the obtained value. Then we will simplify the obtained value to find the required value.

Complete step-by-step answer:

We are given that cos10cos20cos30...cos900...cos1790

.

Rewriting this above equation, we get

⇒cos10cos20cos30cos40cos50cos60cos70cos80cos90...cos900...cos1790

Using the cosine value cos90=0

, in the above equation, we get

⇒cos10cos20cos30cos40cos50cos60cos70cos80×0×...cos900...cos1790

Multiplying the above values, we get

⇒0

Thus, the value of cos10cos20cos30...cos900...cos1790

is 0.

hope it helps you ✌️✅✅

Answer 2

Answer:

cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (360°) = 0

Step-by-step explanation:

To find,

cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (360°)​

Recall the formula

cos (180 + Ф) = -cosФ

Solution:

cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (360°)

= cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (180°)+

+cos (180+10) + cos (180+20°) + cos (180+30°)+ ... + cos (180+180°)

Applying the formula cos (180 + Ф) = -cosФ

=  cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (180°)

-cos (10) - cos (20°) - cos (30°) - cos (40) + ... - cos (180°)

=0

∴cos (10) + cos (20°) + cos (30°) + cos (40) + ... + cos (360°) = 0

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