sin ^2 30°-cos^2 30°
Answers
Step-by-step explanation:
We start by defining sine and cosine.
sin
θ
=
opposite
hypotenuse
and
cos
θ
=
adjacent
hypotenuse
. We use the special triangle above to apply the ratio to the given angles.
30
˚
is opposite the side measuring
1
and adjacent the side measuring
√
3
. The triangle has a hypotenuse of
2
.
So,
sin
30
˚
=
1
2
and
cos
30
˚
=
√
3
2
.
We can now calculate the value of
(
sin
30
)
2
+
(
cos
30
)
2
.
(
sin
30
˚
)
2
+
(
cos
30
˚
)
2
=
(
1
2
)
2
+
(
√
3
2
)
2
=
1
4
+
3
4
=
4
4
=
1
Note that we could also have used the pythagorean identity
sin
2
θ
+
cos
2
θ
=
1
to solve this problem.
Hopefully this helps!
❤gentryamansharma ❤
Answer:
The value of sin 30°= 1/2
The value of cos 30° = root3/2
When we substitute these values in the question :
sin^2 30° = 1/4 and cos ^2 30°= 3/4
Now, sin^2 30° - cos^2 30° =
1/4 - 3/4=
-2/4
-1/2
Therefore the value of sin^2 30° - cos ^2 30° is
-1/2
Hope it helps!!!
Thank you.. ❤️