Question

If sin 0 + cos eco = 2, then the value of
sin power 8 theta + cos ec power 8 theta is equal to:
(B) 2
(C) 2 power8
(D) more than 2power 8
(A) 2 power4
​

Answer 1

(instead of θ, I use A,. It takes time,.)

Answer:

Step-by-step explanation:

Given :

If sin A + cosec A = 2, then the value of

sin⁸ A + cosec⁸ A is equal to

Solution :

We know that,

$cosecA = \frac{1}{sinA}$

So,

sin A + cosec A = 2

⇒ $sinA+\frac{1}{sinA} = 2$

⇒ $\frac{sin^2A+1}{sinA} = 2$

⇒ $sin^2A+1 = 2sinA$

⇒ $sin^2A - 2sinA + 1 = 0$

⇒ $sin^2A - sinA - sinA + 1 = 0$

⇒ $sinA(sinA - 1) -1 (sinA - 1) = 0$

⇒ $(sinA - 1)(sinA - 1) = 0$

⇒ $(sinA - 1)^2 = 0$

⇒ $sinA - 1 = 0$

⇒ $sinA = 1$

⇒ A = 90°

So,

$cosec A = \frac{1}{sinA} = \frac{1}{1} =1$

__

⇒ sin⁸ A + cosec⁸ A

⇒ (1)⁸ + (1)⁸

⇒ 1 + 1 = 2