Question

Verify:cos(2A)=(cotA-tanA)/cscAsecA​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

cot A = $\frac{cosA}{sinA}$, tanA = $\frac{sinA}{cosA}$, cscA  = $\frac{1}{sinA}$, secA = $\frac{1}{cosA}$

Consider the right side

$\frac{cotA-tanA}{cscAsecA}$

= $\frac{\frac{cosA}{sinA}-\frac{sinA}{cosA} }{\frac{1}{sinA}.\frac{1}{cosA} }$

= $\frac{\frac{cos^2A-sin^2A}{sinAcosA} }{\frac{1}{sinAcosA} }$

= $\frac{cos^2A-sin^2A}{sinAcosA}$ × sinAcosA ( cancel sinAcosA )

= cos²A - sin²A

= cos2A

= left side ⇒ verified