1
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
For any $$\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$$, the expression

$$3{(\cos \theta - \sin \theta )^4}$$$$+ 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta$$

equals :
A
13 – 4 cos2$$\theta$$ + 6sin2$$\theta$$cos2$$\theta$$
B
13 – 4 cos6$$\theta$$
C
13 – 4 cos2$$\theta$$ + 6cos2$$\theta$$
D
13 – 4 cos4$$\theta$$ + 2sin2$$\theta$$cos2$$\theta$$
2
JEE Main 2017 (Offline)
+4
-1
If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$,

then the value of $$\cos 4x$$ is :
A
$${1 \over 3}$$
B
$${2 \over 9}$$
C
$$- {7 \over 9}$$
D
$$- {3 \over 5}$$
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
If  m and M are the minimum and the maximum values of

4 + $${1 \over 2}$$ sin2 2x $$-$$ 2cos4 x, x $$\in$$ R, then M $$-$$ m is equal to :
A
$${{15} \over 4}$$
B
$${{9} \over 4}$$
C
$${{7} \over 4}$$
D
$${{1} \over 4}$$
4
JEE Main 2014 (Offline)
+4
-1
Let $$f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ where $$x \in R$$ and $$k \ge \,1.$$
Then $${f_4}\left( x \right) - {f_6}\left( x \right)\,\,$$ equals :
A
$${1 \over 4}$$
B
$${1 \over 12}$$
C
$${1 \over 6}$$
D
$${1 \over 3}$$
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