Question

$\sqrt{1 - sina \div 1 + sina}$
prove that seca-tana

Answer 1

√1-sina÷1+sina

by rationalizing
=√1-sina/1+sina×1-sina/1-sina
=√(1-sina)^2/1^2-sina^2
=√(1-sina)^2/1-sina^2
=√(1-sina)^2/cosa^2
by applying Root on numerator and denominator
= (1-sina)/cosa
=1/cosa-sina/cosa
= seca - tana