cos^A + sin^ = 1 , how?
Answers
Step-by-step explanation:
Explanation:
Assuming you mistyped and meant
sin
−
1
(
cos
(
x
)
)
or simply
arcsin
(
cos
(
x
)
)
, we can easily solve this by putting it on terms of the sine function.
We know that the cosine function, is nothing more than the sine
π
2
radians out of phase, as proved below:
cos
(
θ
−
π
2
)
=
cos
(
θ
)
cos
(
−
π
2
)
−
sin
(
θ
)
sin
(
−
π
2
)
cos
(
θ
−
π
2
)
=
cos
(
θ
)
⋅
0
−
(
−
sin
(
θ
)
sin
(
π
2
)
)
cos
(
θ
−
π
2
)
=
sin
(
θ
)
⋅
1
=
sin
(
θ
)
So we can say that the sine function, 90 degrees ahead, is the cosine function.
arcsin
(
cos
(
x
)
)
=
arcsin
(
sin
(
x
+
π
2
)
)
Using the property of inverse functions that
f
−
1
(
f
(
x
)
)
=
x
, we have
arcsin
(
cos
(
x
)
)
=
x
+
π
2
If you must use degrees, just convert those
π
2
radians to
90
º
degrees.
Answer:
Cos^ + sin^ = 1
Step-by-step explanation:
Sin theta =b/c (opposite side /hypotenuse)
Cos theta =a/c (adjacent side /hypotenuse)
Sin ^theta +cos ^theta = b^/c^ +a^/c^ =a^+b^/c^
By pythagoras theorem
C^=a^+b^
. : cos ^+ sin ^=1