If 4n- - then - 2- 3- - 2n-1- is equal to

The correct option is A 1 cotα .cot2α .cot3α ...cot( 2n 1 ) α = cosα .cos2α .cos3α ...cos( 2n 1 ) α nbsp; sinα .sin2α .sin3α ...sin( 2n 1 ) α nbsp ...

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Byju's Answer

Standard XII

Mathematics

Circular Measurement of Angle

If 4nα =π t...

Question

If $4 n α = π$ then $cot α \cdot cot 2 α \cdot cot 3 α \cdot . . . cot (2 n - 1) α$ is equal to

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none of these

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Solution

The correct option is A 1
$c o t α . c o t 2 α . c o t 3 α . . . c o t (2 n - 1) α = \frac{c o s α . c o s 2 α . c o s 3 α . . . c o s (2 n - 1) α}{s i n α . s i n 2 α . s i n 3 α . . . s i n (2 n - 1) α} = \frac{c o s \frac{π}{4 n} c o s \frac{2 π}{4 n} c o s \frac{3 π}{4 n} . . . c o s \frac{(2 n - 1) π}{4 n}}{s i n \frac{π}{4 n} s i n \frac{2 π}{4 n} s i n \frac{3 π}{4 n} . . . s i n \frac{(2 n - 1) π}{4 n}} = \frac{c o s \frac{π}{4 n} c o s \frac{2 π}{4 n} c o s \frac{3 π}{4 n} . . . c o s \frac{n π}{4 n} . . . s i n \frac{3 π}{4 n} s i n \frac{2 π}{4 n} s i n \frac{π}{4 n}}{s i n \frac{π}{4 n} s i n \frac{2 π}{4 n} s i n \frac{3 π}{4 n} . . . s i n \frac{n π}{4 n} . . . c o s \frac{3 π}{4 n} c o s \frac{2 π}{4 n} c o s \frac{π}{4 n}} = 1$

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Similar questions

Q. If

4 n α = π

, then the value of

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If 4nα=π then cotα⋅cot2α⋅cot3α⋅...cot(2n−1)α is equal to

If $4 n α = π$ then $cot α \cdot cot 2 α \cdot cot 3 α \cdot . . . cot (2 n - 1) α$ is equal to