Question

prove that: 1+sinA-cosA/1+sinA+cosA=1-cosA/1+cosA​

Answer 1

Step-by-step explanation:

Taken LHS

1+sinA-cosA/1+sinA+cosA

according to formula

(a+b+c)²=a²+b²+c²+2ab+2bs+2ca

then;

= 1+sin²A+cos²A+2sinA-2sinAcosA-2cosA/ 1+sin²A+cos²A+2sinA+2sinAcosA+2cosA

= 1+1+2sinA-2cosA-2sinAcosA/1+1+2sinA+2cosA+2sinAcosA

= 2+2sinA-2cosA-2sinAcosA/2+2sinA+2cosA+2sinAcosA

= 2[1+sinA-cosA-sinAcosA]/2[1+sinA+cosA+cosAsinA

= 1+sinA-cosA-sinAcosA/1+sinA+cosA+cosAsinA

= 1(1+sinA)-cosA(1+sinA)/1(1+sinA)+cosA(1+sinA)

= (1+sinA)(1-cosA)/(1+sinA)(1+cosA)

then

1-cosA/1+cosA