Question

PROVE THAT : tan A + cot A = sec A cosec A
Prove the above identity by ALGEBRAICALLY and not by GEOMETRICALLY.
N o t e : L.H.S. = R.H.S.

Answer 1

Answer:

Step-by-step explanation:

Given :

Prove: tan A + cot A = sec A cosec A

Solution :

We know that,

$tanA= \frac{sinA}{cosA}$,

$cotA=\frac{cosA}{sinA}$,

$secA=\frac{1}{cosA}$,

$coseccA=\frac{1}{sinA}$

&

sin² A + cos² A = 1

Hence,

LHS = $tanA+cotA$

⇒ $\frac{sinA}{cosA} + \frac{cosA}{sinA}$

⇒ $\frac{sin^2A+cos^2A}{sinAcosA}$

⇒ $\frac{1}{sinAcosA} = (\frac{1}{sinA})(\frac{1}{cosA} ) = cosecAsecA$ = RHS

Hence, Proved