If sec alpha=5/4, verify that tan alpha/1+tan^2alpha= sin alpha/sec alpha.
Answers
Answer:
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Answer:
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Step-by-step explanation:
We have ,
secα=
base
Hypotenuse
=
4
5
so , we draw a right triangle ABC , right angled at B such that
∠ BAC = α , base = AB = 4 and Hypotenuse = AC = 5
By pyathagoras theorem , we have
AC
2
=AB
2
+BC
2
⇒5
2
=4
2
+BC
2
⇒=BC
2
=25−16=9
⇒ BC = 3
∴tanα=
AB
BC
=
4
3
andsinα=
AC
BC
=
5
3
now
1+tan
2
α
tanα
=
1+(
4
3
)
2
4
3
=
1+
16
9
4
3
=
16
16+9
4
3
=
16
25
4
3
=
4
3
×
25
16
=
25
12
and
secα
sinα
=
5/4
3/5
=
5
3
×
5
4
=
15
12
∴
1+tan
2
α
tanα
=
secα
sinα