Question

Prove that Cot ϴ + Tan ϴ = Cosec ϴ x Sec ϴ

Answer 1

cotϴ + Tanϴ = Cosecϴ × Secϴ

$\frac{ \cosϴ}{ \sinϴ} + \frac{ \sinϴ }{ \cosϴ } = \frac{1}{ \sinϴ } \times \frac{1}{ \cosϴ }$

$\frac{ { \cosϴ }^{2} + { \sinϴ}^{2} }{ \sinϴ \times \cosϴ} = \frac{1}{ \sinϴ } \times \frac{1}{ \cosϴ }$

${ \cosϴ }^{2} + { \sinϴ}^{2} = 1$

$\frac{1}{ \sinϴ } \times \frac{1}{ \cosϴ } = \frac{1}{ \sinϴ } \times \frac{1}{ \cosϴ }$

Hence RHS = LHS.