Step by step solution to "Prove that sec⁡(θ)+csc⁡(θ)=(sin⁡(θ)+cos⁡(θ))(tan⁡(θ)+cot⁡(θ))"

mattgondek4

Answered question

2021-01-07

Prove that

\sec (θ) + \csc (θ) = (\sin (θ) + \cos (θ)) (\tan (θ) + \cot (θ))

SchepperJ

Skilled2021-01-08Added 96 answers

RHS

= (\sin (t) + \cos (t)) \cdot (\tan (t) + \cot (t)) = (\sin (t) + \cos (t)) \cdot (\frac{\sin (t)}{\cos (t)} + \frac{\cos (t)}{\sin (t)}) = (\sin (t) + \cos (t)) \cdot \frac{\sin^{2} (t) + \cos^{2} (t)}{(\sin (t) . \cos (t))}

RHS

= (\sin (t) + \cos (t)) \cdot \frac{1}{(\sin (t) . \cos (t)) = (\frac{1}{\cos (t)} + \frac{1}{\sin (t)}) = \sec (t) + \csc (t) =}

LHS
RHS = LHS

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