Question

simplify (1+tan2tita)(1-sin tita)(1+sin tita )

Answer 1

$(1+tan^2 \theta)(1-sin \theta)(1+sin \theta)\\ \\=(sec^2 \theta)(1-sin \theta)(1+sin \theta)\\ \\=(sec^2 \theta)(1-sin^2 \theta)\\ \\=(sec^2 \theta)(cos^2 \theta)\\ \\= \frac{cos^2 \theta}{cos^2 \theta} \\ \\ =\boxed 1$

Answer 2

(1+tan^2,theta) (1-sin theta)(1+sin theta)=

1+tan^2theta=sec^2theta

(1-sin theta) (1+sin theta)= 1-sin^2 theta

(a-b) (a+b)= (a^2-b^2)

1-sin^2theta=cos^2theta

So sec^2 theta×cos^theta=1

(Sec^2theta=1),.( Cos^2theta=1)