Question : If $\sin^{4} x + \sin^{2} x = 1$ , then what is the value of $\cot^{4} x + \cot^{2} x$ ?
Option 1: –2
Option 2: 2
Option 3: –1
Option 4: 1

Question

Question : If $2 x - 3 (4 - 2 x) < 4 x - 5 < 4 x + \frac{2 x}{3}$ , then $x$ can take which of the following values?
Option 1: 2
Option 2: 8
Option 3: 0
Option 4: –8

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Answer 1

Correct Answer: 1

Solution : Given: $\sin^{4} x + \sin^{2} x = 1$
⇒ $\sin^{4} x = 1 - \sin^{2} x$
By using the trigonometric identity: $\cos^{2} x = 1 - \sin^{2} x$
⇒ $\sin^{4} x = \cos^{2} x$
Dividing both sides by $\sin^{2} x$
⇒ $\frac{\sin^{4} x}{\sin^{2} x} = \frac{\cos^{2} x}{\sin^{2} x}$
⇒ $\sin^{2} x = \cot^{2} x$ ..................(1)
$∴ \sin^{4} x = \cot^{4} x$ ..............(2)
So, $\cot^{4} x + \cot^{2} x = \sin^{4} x + \sin^{2} x = 1$
Hence, the correct answer is 1.

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Question : If sin4⁡x+sin2⁡x=1, then what is the value of cot4⁡x+cot2⁡x?Option 1: –2Option 2: 2Option 3: –1Option 4: 1

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Question : If $\sin^{4} x + \sin^{2} x = 1$ , then what is the value of $\cot^{4} x + \cot^{2} x$ ?
Option 1: –2
Option 2: 2
Option 3: –1
Option 4: 1