If radic 5 tan theta 5 sin theta then what is the value of sin2 theta cos2 theta ........

Quantitative Aptitude (CPO) Trignometry

If √5 tan θ = 5 sin θ, then what is the value of (sin² θ - cos² θ)?

3/5

1/5

4/5

2/5

- We start with the equation: v5 tan ? = 5 sin ?.

- Recall the identity: tan ? = sin ? / cos ?.

- Substitute tan ? in the equation: v5 (sin ? / cos ?) = 5 sin ?.

- Simplify: v5 sin ? = 5 sin ? cos ?.

- Divide both sides by sin ? (assuming sin ? ? 0): v5 = 5 cos ?.

- Solve for cos ?: cos ? = v5 / 5.

- Find sin ? using the Pythagorean identity: sin^2 ? + cos^2 ? = 1.

- Substitute cos^2 ?: sin^2 ? + (5/25) = 1.

- Solve for sin^2 ?: sin^2 ? = 4/5.

- Calculate sin^2 ? - cos^2 ?: 4/5 - 1/5 = 3/5.

- Correct Answer: Option 1, 3/5.

“”

Submit Error