Trig identities help please?

Question

cos² x + (sin x + 1)² / sin x + 1

Answer 1

Substitute 1-sin²x for cos²x, expand your square term and simplify

 

(1-sin²x + sin²x +2sinx+ 1)/(sin x +1)

 

2(sinx + 1)/(sinx + 1) = 2

Answer 2

[cos^2x+(sinx+1)^2]/(sinx+1) is to be simplified ??

(cos^2x+sin^2x+2sinx+1)/(sinx+1)

cos^2x+sin^2x=1

(1+2sinx+1)/(sinx+1)

(2sinx+2)/(sinx+1)

2(sinx+1)/(sinx+1)

2 (answer)