what are the six trig double identities if tanx=2 and cosx<0

Question

I think i got it right, but i want to make sure, any answers would be greatly appreciated

Answer 1

Given tanx = 2

We know that tanx = sinx/cosx

sinx/cosx = 2/1

Opposite side is 2 and adjacent side is 1.

From the pythageron therom hypotenuse = √5

√5^2 = 4+1

5 = 5

Tanx is positive and Cosx is negitive in Q3.

Sinx = -2/√5

Cosx = -1/√5

Sin2x = 2SinxCosx = 2*-2/√5*-1/√5 = 4/5

Cos2x = Cos^2x-Sin^2x = 1/5-4/5 = -3/5

Tan2x = (4/5)/(-3/5) = -4/3

Cot2x = 1/Tan2x = -3/4

Sec2x = 1/Cos2x = -5/3

Csc2x = 1/Sinx = 5/4

 

Comments

Csc2x = 1/Sin2x = 5/4