Mathematics 2002 JAMB Past Questions - Question 31: If tan θ = 4/3, calculate sin22 θ - cos22 θ.

Correct Answer

C

Explanation

Given that tan θ = 4/3, we can use the trigonometric identity:tan² θ + 1 = sec² θRearranging the equation, we have:sec² θ = tan² θ + 1Since sec θ is the reciprocal of cos θ, we can rewrite the equation as:(1/cos² θ) = (4/3)² + 1Simplifying, we get:1/cos² θ = 16/9 + 1          = 16/9 + 9/9          = 25/9Taking the reciprocal of both sides, we have:cos² θ = 9/25Now, using the Pythagorean identity sin² θ + cos² θ = 1, we can find sin² θ:sin² θ = 1 - cos² θ        = 1 - 9/25        = 25/25 - 9/25        = 16/25Therefore, sin² θ - cos² θ = 16/25 - 9/25 = 7/25.