Question

Evaluate -tan²A + 1 + sec²A

Answer 1

Hello :

secA= 1/cosA

tanA = sinA / cosA

- tan²A + 1 + sec²A = - (sinA / cosA)² + 1 + ( 1/cosA)²

= - sin²A / cos²A + 1 + 1 /cos²A

= ( - sin²A + cos²A +1)/cos²A

= ( 1 - sin²A + cos²A ) / cos²A

but : 1 - sin²A = cos²A because : sin²A + cos²A = 1

so : - tan²A + 1 + sec²A = ( 2 cos²A) / (cos²A)

- tan²A + 1 + sec²A = 2

Answer 2

Step-by-step explanation: sec^2A-tan^2A+1

=1+1

=2