find the value of sin 60degree/cos*cos 45degree-
Cot 30degree+15cos90degree
looks like you need to review your basic triangles:
sin 60°/cos^2 45° - cot 30° + 15cos 90°
√3/2 / 1/2 - √3 + 15*0
√3 - √3
0
Sin(theta-30digree)=1/2
To find the value of the given expression: sin 60° / cos45° * cos 45° - cot30° + 15cos90°, we need to evaluate each trigonometric function step by step.
1. Evaluate sin 60°:
The sine of 60° is √3/2.
2. Evaluate cos 45°:
The cosine of 45° is 1/√2 or √2/2.
3. Evaluate cos 45° * cos 45°:
Multiply the cosine of 45° by itself: (√2/2) * (√2/2) = 2/4 = 1/2.
4. Evaluate cot 30°:
To find cot 30°, we need to find the tangent of 30° first. The tangent of 30° is 1/√3 or √3/3. Reciprocating this will give us the cot function, which is √3.
5. Evaluate 15cos90°:
The cosine of 90° is 0, so 15 times 0 is 0.
6. Now, substitute the values back into the expression:
sin 60° / (1/2) - √3 + 0
7. Simplify the expression:
(sin 60°) / (1/2) - √3
= (√3/2) / (1/2) - √3
= (√3/2) * (2/1) - √3
= √3 - √3
= 0
Therefore, the value of the given expression is 0.