Question
If sin⁶ x + cos⁶ x = 7/8, find sin⁴ x +
cos⁴ x:Solution
We know that: sin⁶ x + cos⁶ x = (sin² x + cos² x)(sin⁴ x + cos⁴ x - sin² x cos² x). Since sin² x + cos² x = 1, We get: 1 × (sin⁴ x + cos⁴ x - sin² x cos² x) = 7/8. Now, let sin² x cos² x = z. So, sin⁴ x + cos⁴ x = 1 - 2z. From the equation 1 - 2z –z = 7/8, solving gives: 3z = 1 - 7/8 = 1/8, hence z = 1/24. Thus, sin⁴ x + cos⁴ x = 1 - 2 × 1/24 = 1 - 1/12 = 11/12. Correct option: c) 11/12
A body is said to be in equilibrium when:
Which polymer is used in the production of bullet-proof materials?
Which one among the following statements is not true for Mammals?
Which of the following is a chemical change?
Which vitamin is also known as Vitamin-B2?
If the root mean square speed of gas molecules is doubled, the absolute temperature of the gas:
Which vitamin helps in improving night vision?
Which vitamin is essential for RBC formation?
Which of the following statements for the given chemical reaction is true?
Fe₂ O₃ + 2Al → Al₂ O₃ + 2Fe
The force which opposes the relative motion between different layers of liquid or gases is called –
