Prove that \(\frac{\cos θ}{1 + \sin θ} + \frac{1 + \sin θ}{\cos θ} = 2 \sec θ\).
Proof:
\(\frac{\cos θ}{1 + \sin θ} + \frac{1 + \sin θ}{\cos θ}\)
After taking LCM
After simplifing this then we get,
\(LCM=\)
\(= 2sec\theta\)
\(= \) RHS
Answer variants:
\(2\times \frac{1}{2cos\theta }\)
\(2\times \frac{1}{cos\theta }\)
\(= \frac{(\cos^2 θ + \sin θ^2) + 2 + 2 \sin θ }{(1 + \sin θ)\tan θ}\)
\(= \frac{(\cos^2 θ + \sin θ^2) + 1 + 2 \sin θ }{(1 + \sin θ)\cos θ}\)