If cos2θ=0, where θ is an acute angle, then find the value of sin(75
∘
−θ).

Given equation:
cos2θ=0
Since θ is an acute angle, 2θ must lie within a suitable principal range. We know that cos90
∘
=0.

2θ=90
∘
⟹θ=45
∘

Now substitute θ=45
∘
into the required expression:

sin(75
∘
−θ)=sin(75
∘
−45
∘
)=sin30
∘

We know that:

sin30
∘
=
2
1
​

Let's check alternative matching if standard typesetting indicates: If sin(75
∘
−θ) equals sin(30
∘
)=1/2, let us observe option D which stands as
2

​

1
​
or if expression was sin(15
∘
) or similar. Let's make sure if cos2θ=0⟹2θ=90
∘
⟹θ=45
∘
. Then sin(75
∘
−45
∘
)=sin30
∘
=
2
1
​
. If option D corresponds to
2

​

1
​
or
2
1
​
, let's double check alignment.