Find the value of sin(sin^-1(4/5)+tan^-1(5/12)) without using calculator.Use angle sum or different identities.Kindly help me.
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1
Answer:
Actually it is very easy to find that
sin
(
5
π
12
)
=
√
6
+
√
2
4
.
Explanation:
You use the formula for the sine of a sum:
sin
(
a
+
b
)
=
sin
a
cos
b
+
cos
a
sin
b
Think of a pie divided into twelve slices. Three of them form one quarter, two more form one sixth of the pie. So, thinking of the "pie" as
π
:
5
π
12
=
π
4
+
π
6
.
With that in mind, put
a
=
π
4
,
b
=
π
6
into the sine formula given above:
sin
(
5
π
12
)
=
sin
(
π
4
)
cos
(
π
6
)
+
cos
(
π
4
)
sin
(
π
6
)
Plug in the familiar values
sin
(
π
4
)
=
cos
(
π
4
)
=
√
2
2
,
cos
(
π
6
)
=
√
3
2
,
sin
(
π
6
)
=
1
2
, and you get the answer given above. And, yes, putting that expression into a calculator gives
0.9659
(four significant digits).
Step-by-step explanation:
hope it will be helpful to you dear
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