Correct Answer - Option 1 : 2207
Given:
SinA + CosecA = 3
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
As we know,
SinA = 1/CosecA
⇒ SinA + 1/SinA = 3 ----(1)
Let SinA be x.
Equation (1) becomes,
⇒ x + 1/x = 3
Squaring on both sides,
⇒ (x + 1/x)2 = 32
⇒ x2 + 1/x2 + 2x × 1/x = 9
⇒ x2 + 1/x2 = 9 - 2 = 7
Again,squaring on both sides,
⇒ (x2 + 1/x2)2 = 72
⇒ x4 + 1/x4 = 49 - 2
⇒ x4 + 1/x4 = 47
Again squaring on both sides,
⇒ (x4 + 1/x4)2 = 472
⇒ x8 + 1/x8 = 2209 - 2
Now, Sin8A + 1/Sin8A = 2207
∴ The value of Sin8A + Cosec8A is 2207.