"Verify the identity: (cot⁡(θ)+1)(cot⁡(θ)+1)csc⁡θ=csc⁡(θ)+2cos⁡(θ)" was answered by our community

texelaare

Answered question

2021-09-14

Verify the identity:

\frac{(\cot (θ) + 1) (\cot (θ) + 1)}{\csc θ} = \csc (θ) + 2 \cos (θ)

comentezq

Skilled2021-09-15Added 106 answers

Solution:

\frac{(\cot (θ) + 1) (\cot (θ) + 1)}{\csc θ} = \csc (θ) + 2 \cos (θ)

Taking LHS:

\frac{{(\cos θ + 1)}^{2}}{\csc θ} = \frac{\cot^{2} θ + 2 \cos θ + 1}{\csc θ}

= \frac{\csc^{2} θ + 2 \cos θ}{\csc θ}

= \frac{\csc^{2} θ}{\csc θ} + \frac{2 \cos θ}{\csc θ}

= \csc θ + \frac{2 \cos θ}{\sin θ \cdot \frac{1}{\sin θ}}

= \csc θ + 2 \cos θ = R H S

LHS=RHS
Hence proved

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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