Cos plus tansin equals sec

Answer 1

Start on the left-hand side.

cos(x) + tan(x)sin(x)

Put tan(x) in terms of sin(x) and cos(x).

cos(x) + [sin(x)/cos(x)]sin(x)

Multiply.

cos(x) + sin2(x)/cos(x)

Make the denominators equal.

cos2(x)/cos(x) + sin2(x)/cos(x)

Add.

[cos2(x) + sin2(x)]/cos(x)

Use the Pythagorean Theorem to simplify.

1/cos(x)

Since 1/cos(x) is the same as sec(x)- the right-hand side- the proof is complete.