Question

Number of values of theta(0,3pie) satisfying both the equation 2sin^2 theta+sin^2 2theta =2 and sin 2theta +cos 2theta=tan theta is​

Answer 1

Answer:

We have 2sin

2

x+sin

2

2x=2

2sin

2

x+(2sinxcosx)

2

=2

2sin

2

xcos

2

x+sin

2

x=1

2sin

2

xcos

2

x−(1−sin

2

x)=0

2sin

2

xcos

2

x−cos

2

x=0

cos

2

x(2sin

2

x−1)=0

cos

2

x=0 or sin

2

x=

2

1

⇒ x=2nπ+

2

π

sin

2

x=sin

2

4

π

=2nπ+

2

π

or x=mπ±

4

π

, m∈Z, where m,n∈Z