Question

cosecA-2cot2AcosA=2sinA. plz prove it

Answer 1

hey pratham here your answer if you setesfie please mark it brainliest

Answer 2

Answer:

Step-by-step explanation:

$cosecA-2cosAcot2A$

⇒$cosecA-2cosA\times\frac{cos2A}{sin2A}$

⇒$cosecA-2\frac{cosA}{tan2A}$

Using $tan2A=(\frac{2tanA}{1-tan^{2}A})$,

⇒$cosecA-\frac{cos^{2}A(1-tan^{2}A)}{tanA}$$cosecA-\frac{cos^{2}A(1-tan^{2}A)}{sinA}$

⇒$\frac{1}{sinA}-\frac{cos^{2}A}{sinA}+sinA$

⇒$\frac{1-cos^{2}A+sin^{2}A}{sinA}$

We know that $1-cos^{2}A=sin^{2}A$

⇒$\frac{sin^{2}A+sin^{2}A}{sinA}$

⇒$\frac{2sin^{2}A}{sinA}$

⇒$2sinA$

Hence proved.