If x = 30 degree verify that tan 2x = 2 tan x / 1 - tan^2 x
Answers
Answered by
0
Answer:
Step-by-step explanation:
tan
x
=
sin
x
cos
x
,
sin
2
x
=
2
sin
x
cos
x
and
cos
2
x
=
cos
2
x
−
sin
2
x
, for the right hand side expression
Explanation:
2
tan
x
1
−
tan
2
x
=
2
sin
x
cos
x
1
−
(
sin
2
x
cos
2
x
)
=
2
sin
x
cos
x
cos
2
x
−
sin
2
x
=
sin
2
x
cos
2
x
=
tan
2
x
Proofs for
sin
2
x
=
2
sin
x
cos
x
and
cos
2
x
=
1
−
2
sin
2
x
:
Use
Area of a
△
ABC = 1/2(base)(altitude) = 1/2 bc sin A. Here,
it is the
△
ABC of a unit circle, with center at A, B and C on
the circle and
∠
A = 2x. Here, AB = AC = 1, BC = 2 sinx and
the altitude from A, AN = cos x.
Area of
△
ABC = 1/2 (BC) (AN) = 1/2(OA)(OB) sin A.
Readily, 1/2(2 sin x) cos x = 1/2 (1)(1)sin 2x.
Use
a
2
=
b
2
+
c
2
−
2
b
c
cos
A
, to get the cosine formula.
graph{(x^2+y^2-1)(y-x)(y+x)(x-0.707)=0[0 3 -0.73 0.73]}
Answered by
5
Answer:
the solution is in attachment hope it helps
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