LetP be the point of intersection of the lines x + 3 y-1 = 0 and 3 x-y + 1 = 0, then the line passing through the points C a n d P also passes through the point: Q. If a = i − j + k , a ⋅ b = 0 , a × b = c , , where c = − 2 i − j + k , then b is equal to Applythe trig identity: sin (a - b) = sin - sin b.cos a sin (180 - a) = sin 180.cos a - sin a.cos 180 Since sin 180 = 0 and cos 180 = -1, there for Trigonometryquestions and answers. Consider the following formulas. a sin Bθ + b cos Bθ = a2 + b2 sin (Bθ + C), where C = arctan (b/a) and a > 0 a sin Bθ + b cos Bθ = a2 + b2 cos (Bθ − C), where C = arctan (a/b) and b > 0 Use the formulas given above to write the trigonometric expression in the form a sin Bθ + b cos Bθ. 11 cos (θ Anothermethod to derive the value of sineo 120 degrees is by using cosine functions. With the help of the trigonometry formula, sino (90 + a) = coso a ,we can determine sin 120 exact value. As we know, sino (90° + 30°) = sino 120 degrees. Hence, sin 120 degree = cos 30°. As we know the value of cos 30° is equal to. 5Answers. For x ∈ [0, π], the function f(x) = sin(x) is concave, so by Jensen's inequality, we have 1 3f(A) + 1 3f(B) + 1 3f(C) ≤ f[1 3(A + B + C)] = sin(π / 3) = √3 2. Equality is achieved when A = B = C = π / 3. Note that sinB + sinC = 2sinB + C 2 cosB − C 2. Ineed to prove or disprove that in any acute $\triangle ABC$, the following property holds: $$\sin A + \sin B + \sin C \gt \cos A + \cos B + \cos C$$. To begin, I proved a lemma: Lemma. An acute triangle has at most one angle which is less than or equal to $\dfrac{\pi}{4}$.. Proof: Thecorrect option is B 4 sin A sin B sin C G.E = 2 sin(A+B) cos (A B) + 2 sin C cos C = 2 sin C (cos (A - B) - cos (A + B)) = 4 sin A sin B sin C. Suggest Corrections cos A ( sin B . cos C - cos B . sin C ) + cos B ( sin C . cos A - cos C . sin A ) + cos C ( sin A . cos B - cos A . sin B ) use the basic trigonometry formula of sin(A-B) Advertisement Advertisement New questions in Math. the number of the digit in the square root of the 7 digit square is Stepby step video & image solution for Prove that sin(A+B)sin(A-B)=sin^(2)A-sin^(2)B by Maths experts to help you in doubts & scoring excellent marks in Class 11 exams. Class 11 MATHS TRIGONOMETRIC FUNCTIONS Stepby step video & image solution for In any DeltaABC, prove that (sin B)/(sin C) = (c-a cos B)/(b-a cos C) by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Class 12 MATHS SINE AND COSINE FORMULA - FOR BOARDS LAvNu.