Match The Letter with equations to their correct solution

Question

The expressions A,B,C,D and E are left hand sides of identities. The expressions 1,2,3,4 and 5 are right hand side of identities. Match each letter to their correct number.

A.Tan(x)

B.Cos(x)

c.Sec(x)*CSC(x)

D.(1-(Cos(x)))^2/Cos(x)

E.2*Sec(x)

1.Sin(x)*Tan(x)

2.(cos(x)/1-Sin(x))+(1-Sin(x)/Cos(x))

3.Tan(x)+Cot(x)

4Sin(x)*Sec(x)

5.Sec(x)-Sec(x)*(Sin(x))^2

Answer 1

There are two key things you can use to solve these:

1) convert to sines and cosines

2) get common denominators and combine fractions.

For instance on problem 1, convert tan(x) into sin(x)/cos(x). Then, multiplying by sin(x) you get sin²(x)/cos(x). Then use the Pythagorean Identity sin²(x) + cos²(x) = 1 but modify it to be sin²(x) = 1 - cos²(x) and substitute "1 - cos²(x)" in place of sin²(x) and you get answer D.

Use these two rules above on the other problems.