Question

prove that (1 + tan²A) + (1 + 1 ÷ tan²A) = 1÷sin²A - sin⁴A​

Answer 1

Answer:

First substitute Value of

Tan²A = Sin²A/Cos²A

Then simplify

Lastly ,Substitute Cos²A = 1 - Sin²A

To get your answer

Hope it helps : )

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

L.H.S. = ( 1 + tan² A ) + ( 1 + 1 / tan² A )

= ( 1 + tan² A ) + ( 1 + cot² A )

= ( 1 + sin² A / cos² A ) + ( 1 + cos² A / sin² A )

= ( cos² A + sin² A / cos² A ) + ( sin² A + cos² A / sin² A )

= ( 1 / cos² A ) + ( 1 / sin² A )

= ( sin² A + cos² A ) / sin² A. cos² A

= 1 / sin² A. cos² A

= 1 / sin² A ( 1 - sin² A )

= 1/ sin² A - sin⁴ A

= R.H. S

Hence it is proved