Question

Prove that
tanA+cotA=2 cosec A

Answer 1

Step-by-step explanation:

To prove:

tanA + cotA = 2cosecA

Proof:

L.H.S = tanA + cotA

=> $\frac{sinA}{cosA} + \frac{cosA}{sinA}$

[since tanA = sinA/cosA and cotA = cosA/sinA]

$\frac{sin^2A + cos^2A}{sinA \times cosA}$

$\frac{1}{sinA \times cosA}$ [since sin^2A + cos^2A = 1]

Multiplying by 2 on both numerator and denominator,

$\frac{1 \times 2}{2(sinA \times cosA)}$

$\frac{2}{2(sinA \times cosA)}$

We know that,

2sinA × cosA = sinA

$\frac{2}{2sinA}$

$2 \times \frac{1}{sinA}$

$2 \times cosecA$

=> 2cosecA

L.H.S = R.H.S

$\boxed{\pink{\mathsf{\therefore tanA + cotA = 2cosecA}}}$

Hence, the proof.