Question:
prove that y=4sin(theta)/(2 cos(theta))-theta is an increasing func in range[0,pi/2]
Answer:
Let f(θ) = 4sin θ/(2 * cos θ) - θ
=> f(θ) = 2tan θ - θ
Now, df(θ)/dx = 2sec2 θ - 1
Since, df(θ)/dθ = 2sec2 θ - 1 > 0 for x ∈ [0, π/2]
So, 4sin θ/(2 * cos θ) - θ is an increasing function for x ∈ [0, π/2]
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