Question

If SinA + CosecA = 3 then what will be the value of Sin⁸A + Cosec⁸A ?

1. 2207
2. 47
3. 7
4. 2209

Answer 1

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.