Question

If cos e +sin” =m, then
a) 1<m < 2
b) 1/2<m<1
c) 3/4<m <1
d) 3/4<m<13/16​

Answer 1

Answer:

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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)

=1−

4

1

.1=

4

3

Max.(A)=1−

4

1

.Min.(sin

2

2θ)

=1−

4

1

.0=1

∴

4

3

≤A≤1

Hence, option 'B' is correct.