Let f: R → R be defined as f(x+y)+f(x-y) = 2f(x)f(y), f(1/2) = -1. Then, the value of Σ₂₀_(k=_1) 1/(sin(k)sin(k+f(k))) is equal to :
Let f: R → R be defined as f(x+y)+f(x-y) = 2f(x)f(y), f(1/2) = -1. Then, the value of Σ₂₀_(k=_1) 1/(sin(k)sin(k+f(k))) is equal to :
Option 1 -
cosec²(21)cos(20)cos(2)
Option 2 -
sec²(1)sec(21)cos(20)
Option 3 -
sec²(21)sin(20)sin(2)
Option 4 -
cosec²(1)cosec(21)sin(20)
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1 Answer
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Correct Option - 1
Detailed Solution:
Similar Questions for you
Let
Given ...(1)
∴ x1 + z1 = 2 … (2)
x2 + z2 = 0 … (3)
x3 + z3 = 0 … (4)
Given
⇒ – x1 + z1 = −4 … (5)
–x2 + z2 = 0 &nbs
g (x) = px + q
Compare 8 = ap2 …………… (i)
-2 = a (2pq) + bp
0 = aq2 + bq + c
=>4x2 + 6x + 1 = apx2 + bpx + cp + q
=> Andhra Pradesh = 4 ……………. (ii)
6 = bp
1 = cp + q
From (i) & (ii), p = 2, q = -1
=> b = 3, c = 1, a = 2
f (x) = 2x2 + 3x + 1
f (2) = 8 + 6 + 1 = 15
g (x) = 2x – 1
g (2) = 3
Kindly consider the following figure
B = (I – adjA)5
Kindly consider the following figure
B = (I – adjA)5
System of equation is
R1 – 2 R2, R3 – R2
System of equation will have no solution for = -7.
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