Question

if sin theta =m/n. then find tan theta + 4/ 4 cot theta + 4​

Answer 1

Step-by-step explanation:

sinθ=m/n

∴, cosθ=√1-sin²θ=√1-m²/n²=√(n²-m²)/n²=√(n²-m²)/n

∴,tanθ=sinθ/cosθ=m/√(n²-m²)

cotθ=1/tanθ=√(n²-m²)/m

∴, (tanθ+4)/(4cotθ+1)

=[m/√(n²-m²)+4]/[4√(n²-m²)/m+1]

=[{m+4√(n²-m²)}/√(n²-m²)]/[{4√(n²-m²)+m}/m]

={m+4√(n²-m²)}/√(n²-m²)×m/{m+4√(n²-m²}

=m/√(n²-m²)