Steps to verify sin^2 x (1+cot^2 x) =1

Answer 1

Hi Kennedy,

You can use the trigonometric identities, sin²x + cos²x =1 and tangent x = sin x/cos x, cotangent x = cos x/sin x and substitute them in to simplify:

sin²x X (1 + cos²x / sin²x) = 1 find a common denominator for the terms in parenthesis.

sin²x(sin²x / sin²x + cos²x / sin²x) =1

sin²x(1 / sin²x) =1

1=1

I hope this method is helpful by substituting in trigonometric identities. Feel free to contact me if you have questions.

Answer 2

Hi, Kennedy!

The key to solving this problem is to use the trigonometric identity 1 + cot²(x) = csc²(x):

sin²(x)(1 + cot²(x)) = 1

sin²(x) × csc²(x) = 1

[Here we can also recall that csc(x) = 1/sin(x)]

sin²(x) / sin²(x) = 1

1 = 1

Thus, by using our trigonometric identities, we can prove that the original expression is true.

I hope that this explanation was helpful, and please don't hesitate to reach out if you have any further questions!