Q. 215.0( 1 Vote )

# Solve the follow

3 tan θ + cot θ = 5 cosec θ

3 tan θ + (1/tan θ) = 5 cosec θ

Multiply both sides by tan θ:

3tan 2 θ + 1 = 5 cosec θ tan θ

3tan 2 θ + 1 = 5 × (1/sin θ) × (sin θ/cos θ)

3(sec 2 θ - 1) + 1 = 5 (1/cos θ)

(using 1 + tan 2 θ = sec 2 θ)

3(sec 2 θ - 1) + 1 = 5 sec θ

3sec 2 θ - 5sec θ - 2 = 0

sec θ =

sec θ = 2 or (-1/3)
sec θ ≠ (-1/3) as -1 < cos θ <1 )

sec θ = 2

θ = 60° for 0° < θ ≤ 90°.

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