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
63 98 140 192 251 318
...- Find the wrong number in the given number series.
154, 137, 114, 84, 46, 11 63, 124, 215, 345, 511, 728
Find the wrong number in the given number series.
24, 47, 76, 107, 144, 189
14 15 24 50 98 179
...850, 849, 841, 814, 750, 688
121 127 133 142 160 206
...- Find the wrong number in the given number series.
7, 32, 257, 882, 2107, 4132 - Find the wrong number in the given number series.
16, 25, 37, 52, 72, 97 15, 27, 51, 99, 193, 387