Verify the identity

Question

I will use x in place of theta**

tan^2(x/2)= (secx-1)/secx+1

If you use the half-angle formula to rewrite the left side you get:

(1-cosx)/ (1+cosx)

From there, you can multiply the numerator and denominator by sec x

you get:

Sec(x)-sec(x)cos(x) / sec(x)+sec(x)cos(x)

From there, you can simplify to sec(x)-1/sec(x)+1 using which identity?

A)Even-Odd

B)Reciprocal

C)Pythagorean

D)Quotient

Answer 1

Reciprocal

secant and cosine are reciprocals...

so secant TIMES cosine is 1