Question

Prove that tan^2A +cot^2A +2=cosec^2A *sec^2A

Answer 1

Answer:

2a 2a 2 = 2a so it is a answer .

Answer 2

tan² A + cot² A + 2 = csc² A. sec² A

Step-by-step explanation:

★ Given that :

Prove that: tan² A + cot²A + 2 = csc² A. sec² A

★ LHS :

$\sf \implies \tan^{2}\:A + \cot^{2}\:A + 2$

$\sf \implies \tan^{2}\:A + 1+ \cot^{2}\:A + 1$

• tan² A + 1 = sec² A
• cot² A + 1 = csc² A

$\sf \implies \sec^{2}\:A +\csc^{2}\:A$

• sec² A = 1/cos² A
• csc² A = 1/sin² A

$\sf \implies \cfrac{1}{\cos^{2}\:A} + \cfrac{1}{\sin^{2}\:A}$

$\sf \implies \cfrac{\sin^{2}\:A + \cos^{2}\:A}{\cos^{2}\:A\sin^{2}\:A}$

• sin² A + cos² A = 1

$\sf \implies \cfrac{1}{\cos^{2}\:A\sin^{2}\:A }$

$\sf \implies \cfrac{1}{\cos^{2}\:A} \: \: \: . \: \: \: \cfrac{1}{\sin^{2}\:A }$

$\sf \implies \sec^{2}\:A .\csc^{2}\:A$

Hence,LHS = RHS.

IT WAS PROVED.