What does sin(squared)t + cot(squared)tsin(squared)t equal? and can someone explain it?
sin^2 t + (cot^2 t)(sin^2 t)
= sin^2 t + (cos^2 t / sin^2 t)(sin^2 t)
= sin^2 t + cos^2 t
= 1
Thank you very much, that helped a lot
To evaluate the expression sin^2(t) + cot^2(t)sin^2(t), we need to use trigonometric identities.
Let's break down the given expression step by step:
1. Start with the identity cot^2(t) = 1 / tan^2(t).
- This identity relates cotangent to tangent.
2. Now, substitute the expression cot^2(t) with 1 / tan^2(t) in the original expression:
sin^2(t) + (1 / tan^2(t)) * sin^2(t)
3. Simplify the expression by multiplying sin^2(t) with (1 / tan^2(t)):
sin^2(t) + (sin^2(t) / tan^2(t))
4. Use the identity tan^2(t) = sin^2(t) / cos^2(t) to simplify further:
sin^2(t) + (sin^2(t) / (sin^2(t) / cos^2(t)))
5. Simplify the expression by canceling out the sin^2(t):
sin^2(t) + (1 / cos^2(t))
6. Finally, use the identity 1 / cos^2(t) = sec^2(t):
sin^2(t) + sec^2(t)
Hence, the expression sin^2(t) + cot^2(t)sin^2(t) simplifies to sin^2(t) + sec^2(t).