Question

Simplify ( 1+tan²A ) ( 1-sin²A) (1+sin²A)

Answer 1

(1+tan square A)=sec square A
therefore it equals to (sec square A)(cos square A)
sec is reciprocal of cos
therefore it equals to 1/cos square A×cos square A(1+sin square A)
therefore cos will get cancelled...
therefore it equals to( 1+sin square A)

Answer 2

step1: ( 1+tan²A ) ( 1-sin²A) (1+sin²A),

           (1+sin²A/cos²A)(cos²A)(1+sin²A)          (* sin²A+cos²A=1)

             ((cos²A+ sin²A)/(cos²A))(cos²A)(1+sin²A)

               (1)(1+sin² A)

              (1-(-sin² A))

               - cos²A