Question

tantheata+cottheta=sectheta×cosectheta​

Answer 1

Step-by-step explanation:

let x be theta,

LHS = tan(x) + cot(x) = sin(x)/cos(x) + cos(x)/ sin(x)

= ( (sin(x) )^2 + ( cos(x) )^2) / (sin(X)cos(X))

= 1 / sin(x) cos(x)

= cosec(x). sec(x) = RHS

Answer 2

Answer:

$\tan( \alpha ) + \cot( \alpha ) = \sec( \alpha ) \times \cosec ( \alpha ) \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ = \frac{ { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} }{ \sin( \alpha ) \cos( \alpha ) } \\ = \frac{1}{ \sin( \alpha ) \cos( \alpha ) } \\ = \sec( \alpha ) \cosec( \alpha )$