Question

cos 2 theta minus sin 2 theta equal to one make it polar
$cos(2x) - sin(2x) = 1 \: make \: it \: polar$
​

Answer 1

Answer:

f(x)=

∣

∣

∣

∣

∣

∣

∣

∣

1+sin

2

x

sin

2

x

sin

2

x

cos

2

x

1+cos

2

x

cos

2

x

4sin2x

4sin2x

1+4sin2x

∣

∣

∣

∣

∣

∣

∣

∣

=(1+sin

2

x)[(1+cos

2

x)(1+sin

2

x)−4sin2xcos

2

x]+cos

2

x[4sin2xsin

2

x−sin

2

x(1+4sin2x)]+4sin2xsin

2

x(cos

2

x−1−cos

2

x)

=(1+sin

2

x)(1+4sin2x+cos

2

x)+cos

2

x(−sin

2

x)−4sin2xsin

2

x

=1+4sin2x+cos

2

x+sin

2

x+4sin2xsin

2

x−4sin2xsin

2

x+cos

2

xsin

2

x−cos

2

xsin

2

x

=2+4sin2x (sin

2

x+cos

2

x=1)

∴f

′

(x)=

dx

d

(4sin2x+2)=8cos2x

f

′

(x)=0⇒8cos2x=0

∴cos2x=0

2x(2n−1)

2

π

x=(2n−1)

4

π

For max value

f

′

(α)<0

∴

dx

d

(8cos2x)=−16sin2x<0⇒sin2x>0

When cos2x=0⇒sin2x=±1. Since sin2x>0

∴nsin2x=1

Max f(a)=2+4(1)=6

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