What number should be subtracted from 4(sin4 60º + cos4 30º) - (tan2 45º - cot2 30º) + cos2 45º - cosec2 45º + sec2 60º to get 2?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 7.
4[(√3/2)⁴ + (√3/2)⁴] - 1 + (√3)² + (1/√2)² - (√2)² + (2)²
⇒ 4[(9/16) + (9/16)] - 1 + 3 + (1/2) - 2 + 4
⇒ (9/2) - 1 + 3 + (1/2) + 2
⇒ 5 + 5 - 1
⇒ 9
Let the number that must be subtracted to get 2 be y
⇒ 9 - y = 2
⇒ y = 7