sin130.tan60 ÷cos540.tan230.sin400
sin130° = sin 50°
tan60° = √3
cos540° = cos180 = -1
tan230° = tan50
sin400= sin40
sin130.tan60 ÷cos540.tan230.sin400
= (sin50°)(√3)/(-1) (tan50)(sin40)
= -√3sin50 (sin50/cos50)(sin40)
= -√3 sin40° sin^2 50° / cos50°
I see nothing special from here.
Were there brackets of sorts ?
I think it was
sin130.tan60 ÷(cos540.tan230.sin400)
= (sin50 √3)/(-1 * sin50/cos50 * sin40)
= -√3 cos50/sin40
But since cos50 = sin40, the result is just
-√3
To simplify the expression sin130.tan60 ÷ cos540.tan230.sin400, we can break it down into smaller parts and simplify each part individually.
Step 1: Calculate the value of sin130 and tan60.
Using a scientific calculator or an online calculator, we find that sin130 ≈ 0.766 and tan60 ≈ 1.732.
So, sin130.tan60 ≈ 0.766 * 1.732.
Step 2: Calculate the value of cos540, tan230, and sin400.
Similarly, using a scientific calculator or an online calculator, we find that cos540 = -1, tan230 ≈ 0.463, and sin400 ≈ -0.189.
So, cos540.tan230.sin400 ≈ -1 * 0.463 * -0.189.
Step 3: Combine the individual parts.
Now, we have: sin130.tan60 ÷ cos540.tan230.sin400
≈ 0.766 * 1.732 / (-1 * 0.463 * -0.189)
Step 4: Simplify further.
To simplify the expression, we divide the numerator (0.766 * 1.732) by the denominator (1 * 0.463 * -0.189).
Using a calculator, we get:
≈ -3.556
Therefore, the simplified value of sin130.tan60 ÷ cos540.tan230.sin400 is approximately -3.556.