Question

evaluate: cos²40°-sin²50°​

Answer 1

First of all, we should assume that
−
135
is degrees, not radians.
Secondly, recall the definition of a function cosine.
Cosine of an angle is an abscissa (X-coordinate) of the point on a unit circle at the end of a radius that makes this angle in the counterclockwise direction from the positive direction of X-axis.
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From this definition and, as seen from the picture, it is obvious that
cos
(
x
)
=
cos
(
−
x
)
and
cos
(
180
o
−
x
)
=
−
cos
(
x
)

Let's now find the value of
cos
(
−
135
o
)
.
From
cos
(
−
x
)
=
cos
(
x
)
follows that
cos
(
−
135
o
)
=
cos
(
135
o
)

From
cos
(
180
o
−
x
)
=
−
cos
(
x
)
follows that
cos
(
135
o
)
=
cos
(
180
o
−
45
o
)
=
−
cos
(
45
o
)
=
−
√
2
2
Hence,
cos
2
(
−
135
o
)
=
(
−
√
2
2
)
2
=
1
2

Answer 2

Answer:

0

sin^2 (90-40) - sin^2(50)

therefore 0