If cos ɵ =
3÷5
then what is the value of 6tan ɵ - 5cos ɵ ?
Answers
Given : cosθ = 3/5
To find : the value of (6tanθ - 5cosθ)
solution : it is given that, cosθ = 3/5 = base/hypotenuse,
so, base = 3 and hypotenuse = 5
from Pythagoras theorem,
hypotenuse² = altitude² + base²
⇒5² = altitude² + 3²
⇒altitude = 4
now, tanθ = altitude/base = 4/3
now 6tanθ - 5cosθ
= 6 × 4/3 - 5 × 3/5
= 8 - 3
= 5
Therefore the value of (6tanθ - 5cosθ) = 5.
6tan ɵ - 5cos ɵ = - 11 or 5 if cos ɵ = 3÷5
Step-by-step explanation:
cos ɵ = 3÷5
Squaring both sides
=> cos ²ɵ = 9÷25
using
cos ²ɵ + sin ²ɵ = 1
9÷25 + sin ²ɵ = 1
=> sin ²ɵ = 16÷25
=> sin ɵ = ± 4÷5
tan ɵ = sin ɵ ÷ cos ɵ
=> tan ɵ = (± 4÷5 ) ÷ (3÷5 )
=> tan ɵ = ± 4÷3
6tan ɵ - 5cos ɵ
= 6 ( ± 4÷3 ) - 5 (3÷5)
= ± 8 - 3
= - 11 or 5
6tan ɵ - 5cos ɵ = - 11 or 5
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