The value of the expression sin x + cosec x = 2, then the value of sin7x + cosec7x is:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 2.
sin x + cosec x = 2
⇒ sin x + (1/sin x) = 2
⇒ sin2x + 1 = 2sin x [Multipling both sides by sin x]
⇒ sin2x - 2sin x + 1 = 0
⇒ (sin x - 1)2 = 0
⇒ sin x - 1 = 0
⇒ sin x = 1 = sin 90°
⇒ x = 90°
Now, sin7x + cosec7x = sin7 90° + cosec7 90° = 17 + 17 = 1 + 1 = 2
Therefore, the value of sin7x + cosec7x is 2.