Ithen did the same thing to the other side to get $$-2(\sin(B+C)\cos(B+C)+\sin(A+C)\cos(A+C)+\sin(A+B)\cos(A+B))$$ and then tried using the compound angle formula to see if i got an equality. However the whole thing became one huge mess and I didn't seem to get any closer to the solution.asin(C) = c·sin(A) Next, draw altitude h from angle A instead of B, as shown below. For the newly formed triangles ADB and CDB, Triangle ADB: Triangle CDB: Setting these two values of h equal to each other: b·sin(C) = c·sin(B) Using the transitive property, we can put these two sets of equations together to get the Law of Sines: and
Thecorrect option is B0 °Consider sin 2 A = 2 sin A.. iWe know that sin 2 A = 2 sin A cos A. i iSubstitute i i in i, we getsin 2 A = 2 sin A ⇒ 2 sin A cos A = 2 sin A ⇒ cos A = 1 b u t cos 0 ° = 1 ⇒ A = 0 °Hence, sin 2 A = 2 sin A is true when A = 0 °. Suggest Corrections. 94.
replacingon the formula of area: $\triangle ABC = 2r^2\sin(a)\sin(b)\sin(c)$ But that doesn't help to answer the question. Is my approach correct, or else, what am I missing? trigonometry; (r^2/2)(\sin (a-b+c) - \sin (a-b-c) - \sin (a+b+c) + \sin (a+b-c))$ Now for the neat part where we use the angle sum being 180°. Then, $\sin (a-b+c \cos (B-A) = \cos B \cos A + \sin B \sin A$ Of course, because of the commutative rule of multiplication, this works out to give you exactly the same expression as the original, i.e. you can rearrange this to: $\cos (B-A) = \cos A \cos B + \sin A \sin B$ By the second way, you can use the property that the cosine function is even. This meanscosβ = cos b sin α = tan a cot c; cos c = cot α cot β = cos a cos b; Napier's rule is a mnemonic for memorizing the above identities. General spherical triangle. For this section we drop the assumption that γ = 90°. Many identities hold. Here are a few examples. Law of sines. sin α / sin a = sin β / sin b = sin γ / sin c. Law ofAnswer One-half b c sine (60 degrees) One-half a squared sine (60 degrees) StartFraction a b sine (60 degrees) Over 2 EndFraction. Explanation: The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides. .