Question

prove that (1+tan²@)(1-sin@)(1+sin@)=1

Answer 1

(1-sin@)(1+sin@) = 1²- sin²@
as cos²@+sin²@ =1
:.1- sin²@ = cos²@

(1+tan²@) = sec²@

so (1+tan²@)(1-sin@)(1+sin@) = sec²@*cos²@ = (1/cos²@)*cos²@ = 1 (proved)