prove that sinx*cosx=cos2x
Answers
Answered by
0
Answer:
Step-by-step explanation:
cos
x
−
sin
x
cos
x
+
sin
x
=
=
[
cos
x
−
sin
x
cos
x
+
sin
x
]
cos
x
+
sin
x
cos
x
+
sin
x
]
=
=
cos
2
x
−
sin
2
x
(
cos
x
+
sin
x
)
2
=
Apply trig identities:
cos
2
x
−
sin
2
x
=
cos
2
x
(
cos
x
+
sin
x
)
2
=
cos
2
x
+
2
sin
x
.
cos
x
+
sin
2
x
=
1
+
sin
2
x
Finally,
cos
x
−
sin
x
cos
x
+
sin
x
=
cos
2
x
1
+
sin
2
x
Answered by
1
Step-by-step explanation:
Use the identity sina+ sinb = sinacosb+cosasinb
let a=b=x
sinx+sinx= sinxcosx+cosxsinx
=2sinxcosx
=cos2x
the above answer is from the identity,
cos2A=2sinAcosA
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