Question

If b = `(3 + cot  π/8 + cot  (11π)/24 - cot  (5π)/24)`, then the value of `|bsqrt(2)|` is ______.

विकल्प

• 6.00

• 7.00

• 8.00

• 9.00

Answer 1

If b = `(3 + cot  π/8 + cot  (11π)/24 - cot  (5π)/24)`, then the value of `|bsqrt(2)|` is 6.00.

Explanation:

Let `π/24` = θ

⇒ `π/8` = 3θ, 8θ = `π/3`,

Given expression cot written as 3 + cot3θ + cot11θ – cot5θ

= `3 + cot3θ + cot(π/3 + 3θ) + (3θ (-π)/3)`

= 3 + 3cot(9θ)

= `3 + 3cot((3π)/8)`

= `3sqrt(2)`

∴ `|bsqrt(2)|` = 6  ...(Formula: cotA + cot(A + 60°) + cot(A – 60°) = 3cot3A)