Question

Prove the trigonometric identity:

$(1 - \ {sin}^{2} \alpha ) {sec}^{2} \alpha = 1$

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Answer 1

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Answer 2

ANSWER :
_________

( 1 - Sin² α ) sec² α = 1

L. H. S. = ( 1 - Sin² α ) sec ² α

IDENTITY USED :
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[ sin² α + cos² α = 1 ]
[ cos² α = 1 - sin² α ]

=> ( cos ² α ) sec² α

=> cos² α × 1 / Cos² α

=> 1.