Question

1-cos2 theata /1+ cos2 theta​

Answer 1

Step-by-step explanation:

I take it that you want another way of stating this expression, preferably one that is simpler.

From the double-angle formula for the cosine function,

Eq. A: cos(2θ)=2cos2(θ)−1

Adding ‘1’ to both sides of Eq. A, we get Eq. B: 1+cos(2θ)=2cos2(θ)

Alternatively, multiplying both sides of Eq. A by ‘-1’ then adding ‘1’ to both sides:

Eq. C: 1−cos(2θ)=2−2cos2(θ)=2[1−cos2(θ)]

Using the trigonometric identity cos2(x)+sin2(x)=1 , we can express Eq. C as: 2sin2(θ)

Applying Eq. B & C to our original expression:

1−cos(2θ)1+cos(2θ)=2sin2(θ)2cos2(θ)=tan2(θ)