Given tan theta = 4/3 and pi< theta< 3pi/2; find cos2theta

-7/25

Step-by-step explanation:

tan θ = 4/3, π < θ < 3π/2

Using double angle formula:

cos (2θ) = (1 - tan²θ) / (1 + tan²θ)

cos (2θ) = (1 - (4/3) ²) / (1 + (4/3) ²)

cos (2θ) = (1 - 16/9) / (1 + 16/9)

cos (2θ) = (9 - 16) / (9 + 16)

cos (2θ) = - 7 / 25