Prove that \(= \)
Proof:
Consider LHS.
LHS \(= (sin \ \alpha + cos \ \alpha)(tan \ \alpha + cot \ \alpha)\)
\(= (sin \ \alpha + cos \ \alpha)\)
\(= (sin \ \alpha + cos \ \alpha)\)
\(= (sin \ \alpha + cos \ \alpha)\)
\(=\)
\(=\)
\(=\)
\(= sec \ \alpha + cosec \ \alpha\)
Hence, we proved.
Answer variants:
\((\frac{sin \ \alpha}{cos \ \alpha} + \frac{cos \ \alpha}{sin \ \alpha})\)
\(\frac{sin \ \alpha + cos \ \alpha}{sin \ \alpha \ cos \ \alpha}\)
\((\frac{sin^2 \ \alpha + cos^2 \ \alpha}{sin \ \alpha \ cos \ \alpha})\)
\((\frac{1}{sin \ \alpha \ cos \ \alpha})\)
\(\frac{sin \ \alpha}{sin \ \alpha \ cos \ \alpha} + \frac{cos \ \alpha}{sin \ \alpha \ cos \ \alpha}\)
\(\frac{1}{cos \ \alpha} + \frac{1}{sin \ \alpha}\)