If 5tanθ=2, then the value of 5sinθ+3cosθ10sinθ−2cosθ is :
Get the complete, step-by-step math solution for: "If 5 tan θ = 2, then the value of (10 sin θ - 2 cos θ)/(5 sin θ + 3 cos θ) is :". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Find the value of tan θ
The problem provides the equation 5tanθ=2. To find the value of tanθ, we simply divide both sides of the equation by 5.
Step 2: Divide numerator and denominator by cos θ
To utilize the value of tanθ, we can divide every term in both the numerator and the denominator of the given expression by cosθ. This transformation will convert the sinθ/cosθ terms into tanθ and simplify the cosθ/cosθ terms to 1.
Step 3: Simplify the expression
After dividing by cosθ, the expression simplifies. The terms cosθsinθ become tanθ, and the terms cosθcosθ become 1.
Step 4: Substitute the value of tan θ
Now, substitute the value of tanθ=52 into the simplified expression. This will allow us to calculate the numerical value of the entire expression.
Step 5: Calculate the final value
Perform the multiplication and then the subtraction in the numerator, and the multiplication and addition in the denominator. Finally, simplify the resulting fraction to get the answer.