If 5 cos 2 2 x -4cos 2 x -sin 4 x -cos 6 x -sin 6 x -8- thenA- sin 2 2 x -3-4B- tan 2 2 x -2017C- cos 2 2 x- 2 2 xD- tan 2 2 xcos 2 2 x- 2 2 xsin 2 2 x

The correct options are C cos^2 2x lt; cot^2 2x D (tan^2 2x)^cos^2 2x=(cot^2 2x)^sin^2 2x 5 cos^2 (2x) + 4(cos^4 x + sin^4 x + cos^6 x + sin^6 x)=8 ⇒ cos ...

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Byju's Answer

Standard XII

Mathematics

Differentiation of Inverse Trigonometric Functions

If 5 cos 2 2 ...

Question

If $5 c o s^{2} 2 x + 4 (c o s^{2} x + s i n^{4} x + c o s^{6} x + s i n^{6} x) = 8$ , then

$s i n^{2} 2 x = \frac{3}{4}$

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$t a n^{2} 2 x > 2017$

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$c o s^{2} 2 x < c o t^{2} 2 x$

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$(t a n^{2} 2 x)^{c o s^{2} 2 x} = (c o t^{2} 2 x)^{s i n^{2} 2 x}$

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Solution

The correct options are
C
$c o s^{2} 2 x < c o t^{2} 2 x$

D
$(t a n^{2} 2 x)^{c o s^{2} 2 x} = (c o t^{2} 2 x)^{s i n^{2} 2 x}$

$5 c o s^{2} (2 x) + 4 (c o s^{4} x + s i n^{4} x + c o s^{6} x + s i n^{6} x) = 8 \Rightarrow c o s 4 x = 0 \Rightarrow 2 c o s^{2} 2 x - 1 = 0 \Rightarrow c o s^{2} (2 x) = \frac{1}{2} = s i n^{2} (2 x)$

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Similar questions

If $\frac{s i n^{4} x}{2} + \frac{c o s^{4} x}{3} = \frac{1}{5}$ , then

\frac{{sin}^{4} x + {cos}^{4} x - 1}{{sin}^{6} x + {cos}^{6} x - 1}

is simplified to

Q. The number of distinct solution of the equation

\frac{5}{4} {cos}^{2} 2 x + {cos}^{4} x + {sin}^{4} x + {cos}^{6} x + {sin}^{6} x = 2

[0, 2 π]

is ?

Q. Assertion :If

e x p {{s i n^{2} x + s i n^{4} x + s i n^{6} x + . . . . . i n f} l o g_{e} 2}

satisfies the equation

x^{2} - 9 x + 8 = 0

, then the value of

\frac{c o s x}{c o s x + s i n x}

\frac{\sqrt{3} - 1}{2} (0 < x < π / 2)

Reason:

s i n^{2} x + s i n^{4} x + s i n^{6} x + . . . .

\infty = s e c^{2} x

f (x) = {sin}^{6} x + {cos}^{6} x

\forall x \in R

, then

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If 5 cos22x+4(cos2x+sin4x+cos6x+sin6x)=8, then

The correct options are C cos22x<cot22x D (tan22x)cos22x=(cot22x)sin22x 5 cos2 (2x)+4(cos4x+sin4 x+cos6 x+sin6 x)=8⇒cos 4x=0⇒2cos22x−1=0⇒cos2(2x)=12=sin2(2x)

If $5 c o s^{2} 2 x + 4 (c o s^{2} x + s i n^{4} x + c o s^{6} x + s i n^{6} x) = 8$ , then