If 8tanA=5, what is the value of
8sinA+11cosA
8sinA−7cosA
?
- A−
8
1
- B19
1
- C8
1
- D−
6
1
Solution & Step-by-step Explanation
Given:
8tanA=5⟹tanA=
8
5
We are required to evaluate the expression:
E=
8sinA+11cosA
8sinA−7cosA
Divide both the numerator and the denominator by cosA:
E=
8
cosA
sinA
+11
8
cosA
sinA
−7
E=
8tanA+11
8tanA−7
Substitute the value 8tanA=5 into the expression:
E=
5+11
5−7
=
16
−2
=−
8
1
8tanA=5⟹tanA=
8
5
We are required to evaluate the expression:
E=
8sinA+11cosA
8sinA−7cosA
Divide both the numerator and the denominator by cosA:
E=
8
cosA
sinA
+11
8
cosA
sinA
−7
E=
8tanA+11
8tanA−7
Substitute the value 8tanA=5 into the expression:
E=
5+11
5−7
=
16
−2
=−
8
1