Question

Find sin2x, cos2x, tan 2x if sec = 13•5

Answer 1

Answer:

Consider the given integral.

∫(sin2x+cos2x)dx=

2

1

sin(2x−a)+C …….. (1)

Now,

I=∫(sin2x+cos2x)dx

I=−

2

cos2x

+

2

sin2x

+C

I=

2

1

[sin2x−cos2x]+C

I=

2

2

[

2

1

sin2x−

2

1

cos2x]+C

I=

2

1

[cos

4

π

sin2x−sin

4

π

cos2x]+C

I=

2

1

sin(2x−

4

π

)+C

On comparing above equation, we get

a=

4

π

,C∈R

Hence, this is the answer.