Question

2. Write the other trigonometric ratios of A in
terms of sec A.​

Answer 1

Step-by-step explanation:

• CosA = 1/SecA

We know,Sin^2 A + Cos^2 A = 1

=>Sin^2 A = 1 - Cos^2 A

=>SinA= root(1-Cos^2 A)

=>SinA= root[1 - (1/SecA)^2]

=>SinA= root[1-(1/Sec^2 A)]

=>SinA= root[(Sec^2 A - 1)/Sec^2 A]

• SinA = root(Sec^2 A - 1) / Sec A

[Note - Here Sec A is not included in root]

CosecA = 1/SinA = 1 ÷ root(Sec^2 A-1) /SecA

• CosecA=SecA/root(Sec^2 A-1)

TanA = SinA/CosA = [root(Sec^2 A-1)/SecA]/(1÷SecA)

• TanA = root(Sec^2 A - 1)

CotA = 1/TanA = 1 ÷ root(Sec^2 A - 1)

• CotA = 1/root(Sec^2 A - 1)