Question

tanA+cotA=secAcosecA​

Answer 1

tanA+cotA = secAcosecA

LHS:-

tanA+cotA

$\frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) }$

$\frac{ \sin {}^{2} (a) + \cos {}^{2} (a) }{ \sin(a) \cos(a) }$

$\frac{1}{ \sin(a) \cos(a) }$

(because we know that,sin²a + cos²a =1)

Now,

$\frac{1}{ \sin(a) } \frac{1}{ \cos(a) }$

$cosec(a)sec(a)$ = RHS

(because, 1/sin (a) = cosec (a)and 1/cos(a) = sec(a))

Cheers!