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