Question

sin^2 45 - sin^2 15​

Answer 1

Step-by-step explanation:

sin²A-sin²B=sin(A+B)sin(A-B)

sin²45-sin²15=sin(45+15)sin(45-15)

=sin60 sin30

= √3/2*1/2=√3÷4

Answer 2

Answer:

To find cos

2

45

o

−sin

2

15

o

We know that, cos2θ=2cos

2

θ−1⟹cos

2

θ=

2

1+cos2θ

And cos2θ=1−2sin

2

θ⟹sin

2

θ=

2

1−cos2θ

∴cos

2

45

o

=

2

1+cos(2×45)

=

2

1+cos90

o

=

2

1+0

=

2

1

Also, ∴sin

2

15

o

=

2

1−cos(2×15)

=

2

1−cos30

o

=

2

1−

2

3

=

2

1

−

4

3

Then we get,

cos

2

45

o

−sin

2

15

o

=

2

1

−

2

1

+

4

3

=

4

3

Hence, cos

2

45

o

−sin

2

15

o

=

4

3