If sin theta=3/4, find the value of 4 tan theta-5 cos theta/sec theta+4 cot theta
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Step-by-step explanation:
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Answer:
We have
sinθ=
5
4
⇒
hypotenuse
perpendicular
=
5
4
so , we contract a right triangle ABC , right angle at B such that ∠BAC=θ , perpendicular = BC = 4 and Hypotenuse = AC = 5
By pythagoras theorem , we have
AC
2
=AB
2
+BC
2
⇒.5
2
=AB
2
+4
2
⇒AB
2
= 25 - 16 = 9
⇒AB=
9
=⇒ AB = 3
∴cosθ=
AC
AB
=
5
3
,tanθ=
AB
BC
=
3
4
cotθ=
AC
AB
=
4
3
,secθ=
AB
BC
=
3
5
∴
secθ+4cotθ
4tanθ−5cosθ
=
3
5
+4×
4
3
4×
3
4
−5×
5
3
=
3
5
+3
3
16
−3
=
3
5+9
3
16−9
=
14
7
=
2
1
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