What are the equivalent expressions of sin(-2x) cos (-3x) cosec(-5x) cot(-7x)?Question 9Answera.-sin(2x)cos(3x)cosec(5x)cot(7x)b.2sin(-x)3cos(-x)5cosec(-x)7cot(-x)c.sin(2x)cos(3x)cosec(5x)cot(7x)d.2sin(x)3cos(x)5cosec(x)7cot(x

The equivalent expressions of sin(-2x) cos (-3x) cosec(-5x) cot(-7x) are -sin(2x)cos(3x)cosec(5x)cot(7x). So, the correct answer is a. -sin(2x)cos(3x)cosec(5x)cot(7x).

Here's why:

1. sin(-2x) is equivalent to -sin(2x) because sine is an odd function, meaning that sin(-θ) = -sin(θ).
2. cos(-3x) is equivalent to cos(3x) because cosine is an even function, meaning that cos(-θ) = cos(θ).
3. cosec(-5x) is equivalent to -cosec(5x) because cosecant is an odd function, meaning that csc(-θ) = -csc(θ).
4. cot(-7x) is equivalent to -cot(7x) because cotangent is an odd function, meaning that cot(-θ) = -cot(θ).

So, putting it all together, sin(-2x) cos (-3x) cosec(-5x) cot(-7x) is equivalent to -sin(2x)cos(3x)cosec(5x)cot(7x).