Question

show that tanA +cotA =2cosec 2A

Answer 1

tanA + cotA = (sinA/cosA) + (cosA/sinA) 
= (sinA.sinA + cosA.cosA)/sinA.cosA 
= 2 (sin²A + cos²A) / 2 sinA.cosA 
= 2 × 1/sin2A 
= 2 cosec2A
LHS=RHS
hence proved

Answer 2

Answer and Explanation :

To show : Expression $\tan A +\cot A =2\csc 2A$

Solution :

Taking LHS,

$\tan A +\cot A$

$=\frac{\sin A}{\cos A}+\frac{\cos A} {\sin A}$

Taking LCM,

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

We know, $\sin^2 A+\cos^2 A=1$

$=\frac{1}{\cos A\times \sin A}$

Multiply and divide by 2,

$=\frac{2}{2\cos A\times \sin A}$

We know, $2\cos A\times \sin A=\sin 2A$

$=\frac{2}{\sin 2A}$

$=2\csc 2A$

= RHS

Therefore, LHS=RHS.