What number should be subtracted from
$4(sin^260° + cos^4 30°) - ( tan^2 45° - cot^2 30°) + cos^2 45° - cosec^2 45° + sec^2 60°$ to get 2 ?
Answer & explanation
Correct answer: option 3
we know, sinA = cosB Iff A + B = 90º
Now,
4 (sin4 60º + cos4 30º ) - ( tan²45º - cot²30º ) + cos²45º - cosec²45º + sec²60º
= 4 ( (√3/2)4 + (√3/2)4 ) - ( 1 - (1/√3)² ) + (1/√2)² - (√2)² + 2²
= 4 ( \(\frac{9}{16}\) + \(\frac{9}{16}\) ) - ( 1 - \(\frac{1}{3}\)) + \(\frac{1}{2}\) - 2 + 4
= 9
ATQ,
Let A is subtracted from 9 to get 2.
9 - A = 2
A = 7