Question

if A=sin28 teta+cos36 teta then (1)0≤A<1 (2)0≤A≤1 (3)0<A≤1 (4)3/4≤A≤1​

Answer 1

Step-by-step explanation:

A=sin

2

θ+cos

4

θ

=sin

2

θ+cos

2

θ.cos

2

θ

=sin

2

θ+cos

2

θ(1−sin

2

θ)

=sin

2

θ+cos

2

θ−sin

2

θcos

2

θ

=1−

4

1

(2sinθcosθ)

2

=1−

4

1

sin

2

2θ

Min.(sin

2

2θ)=0

Max.(sin

2

2θ)=1

Min.(A)=1−

4

1

.Max(sin

2

2θ)

−

4

1

.1=

4

3

Max.(A)=1−

4

1

.Min.(sin

2

2θ)

=1−

4

1

.0=1

∴

4

3

≤A≤1