Practicing Success
If 2 $\frac{cos^2x-sec^2x}{tan^2x}$ = a + b cos 2x, then a, b= ? |
$\frac{-3}{2},\frac{-1}{2}$ $\frac{3}{2},\frac{1}{2}$ -3, -1 3, 1 |
-3, -1 |
2 \(\frac{cos²x - sec²x}{tan²x}\) = 2 \(\frac{(cos²x)² - 1}{sin²x}\) { we know, sin²x + cos²x = 1 } = 2 \(\frac{cos4 x - 1}{1 - cos²x}\) = 2 \(\frac{(cos²x - 1) . (cos²x + 1)}{1 - cos²x}\) = - (2cos²x + 2 ) { using identity, cos²x - 1 = cos 2x } = - ( 1 + cos 2x + 2) = - cos 2x - 3 And ATQ, - cos 2x - 3 = a + b cos2x So, a = -3 and b = -1 Ans :- -3 , -1 |