Civil Engineering: FE Exam with Verified
Solutions
Double Angle Identities ✔️✔️Sin(2x) = 2Sin(x)Cos(x)
Cos(2x) = Cos^2(x) - Sin^2(x)
Cos(2x) = 2Cos^2(x) - 1
Cos(2x) = 1 - 2Sin^2(x)
Tan(2x) = (2Tan(x)) / (1 - Tan^2(x))
Difference Identities ✔️✔️sin(A-B)=sinAcosB-cosAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
Sum Identities ✔️✔️sin(A+B)=sinAcosB+cosAsinB
cos(A+B)=cosAcosB-sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
Co-Function Identities ✔️✔️Cos(π/2 - x) = sin(x)
Sin(π/2 - x)=cos(x)
Cot(π/2 - x)=tan(x)
Tan(π/2 - x)=cot(x)
Csc(π/2 - x)=sec(x)
Sec(π/2 - x)=csc(x)
Solutions
Double Angle Identities ✔️✔️Sin(2x) = 2Sin(x)Cos(x)
Cos(2x) = Cos^2(x) - Sin^2(x)
Cos(2x) = 2Cos^2(x) - 1
Cos(2x) = 1 - 2Sin^2(x)
Tan(2x) = (2Tan(x)) / (1 - Tan^2(x))
Difference Identities ✔️✔️sin(A-B)=sinAcosB-cosAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
Sum Identities ✔️✔️sin(A+B)=sinAcosB+cosAsinB
cos(A+B)=cosAcosB-sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
Co-Function Identities ✔️✔️Cos(π/2 - x) = sin(x)
Sin(π/2 - x)=cos(x)
Cot(π/2 - x)=tan(x)
Tan(π/2 - x)=cot(x)
Csc(π/2 - x)=sec(x)
Sec(π/2 - x)=csc(x)
