Question
If sin x + cos x = 7/5, find sin⁴ x + cos⁴
x:Solution
sin⁴ x + cos⁴ x = (sin² x + cos² x)² - 2sin² x cos² x sin² x + cos² x = 1, and (sin x + cos x)² = 1 + 2sin x cos x = 49/25 So, 2sin x cos x = 24/25 Now, sin² x cos² x = (12/25)² = 144/625 Thus, sin⁴ x + cos⁴ x = 1 - 2 * 144/625 = 1 - 288/625 = 337/625 Correct option: d
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
A boat can travel 30 km upstream and 45 km downstream in 6 hours. Find the speed of the boat in still water if the speed of the stream is 4 km/h.
1219.98 ÷ 30.48 × 15.12 = ? × 2.16
(36.35 × 14.89) ÷ 8.78 = ? – 59.98
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
75.01 + 344.923 - 179.93 = ?3 of (√678 + 3.89)
480.11 ÷ 15.98 × 5.14 – 134.9 = √?
√65 of 14.97 + √50 = (12.02)2 - ?
2380.03 ÷ 84.98 x 39.9 = ? + 15.32
(29.892 × √290) + 32.98 × 6.91 = ?
