Question

Verify the identity. cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x equals two times secant of x.

Answer 1

cos(x)/(1+sin(x) + (1+sin(x))/cos(x)=

cos²(x)/cos(x)(1+sin(x)) + (1+sin(x))²/cos(x)(1+sin(x))=

cos²(x)+1+2sin(x)+sin²(x) /cos(x)(1+sin(x))=

2+2sin(x) / cos(x)(1+sin(x))=

2(1+sin(x)) / cos(x)(1+sin(x))=

2/cos(x)=

2*sec(x)