Question

(sec²A - 1) cot²A = 1

Answer 1

⇒ ( sec²A - 1 ) cot²A = 1

We know that, 

( sec²A - tan²A = 1 )

( ∴ sec²A - 1 = tan²A ).

By substituting this value,

⇒ ( tan²A ) cot²A = 1

⇒ ( 1 / cot²A ) cot²A = 1

 ∴ 1 = 1.

Proved.

Answer 2

Answer:

(sec²A - 1) cot²A = 1

Step-by-step explanation:

To proof : (sec²A - 1) cot²A = 1

Concept :

• tan A = Sin A / Cos A

• cot A = Cos A / Sin A    

• (sec²A - 1) = $tan^{2}A$

Proof :

Given, L.H.S. = (sec²A - 1) cot²A

          We know, (sec²A - 1) = $tan^{2}A$

          So, L.H.S = $tan^{2}A X cot^{2}A$                            (tan A = Sin A / Cos A)

                         =   $(\frac{Sin^{2}A }{Cos^{2}A } )( \frac{Cos^{2}A }{Sin^{2}A })$                          (cot A = Cos A / Sin A)

                        = 1 = R.H.S

                        Hence, proved.

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