If A = 60° and B = 30°, verify that (i) sin(A + B) = sin A cos B + cos A sin B (ii) cos(A + B) = cos A cos B - sin A sin B (iii) sin(A - B) = sin A cos B - cos A sin B (iv) tan(A - B) = tanA-tanB/1+tanAtanB

Question

KnowledgeBoat · Accepted Answer

(i) To verify, sin(A + B) = sin A cos B + cos A sin B Substituting values in L.H.S. of the above equation : sin(A + B) = sin(60° + 30°) = sin 90° = 1. Substituting values in R.H.S. of the equation : sin A cos B + cos A sin B = sin 60° cos 30° + cos 60° sin 30° Since, L.H.S. = R.H.S. Hence, proved that sin(A + B) = sin A cos B + cos A sin B. (ii) To verify, cos(A + B) = cos A cos B - sin A sin B Substituting values in L.H.S. of equation : cos(A + B) = cos(60° + 30°) = cos 90° = 0. Substituting values in R.H.S. of equation : cos A cos B - sin A sin B = cos 60° cos 30° - sin 60° sin 30° Since, L.H.S. = R.H.S. Hence, proved that cos(A + B) = cos A cos B - sin A sin B. (iii) To verify, sin(A - B) = sin A cos B - cos A sin B Substituting values in L.H.S. of equation : sin(A - B) = sin(60° - 30°) = sin 30° = . Substituting values in R.H.S. of equation : sin A cos B - cos A sin B = sin 60° cos 30° - cos 60° sin 30° Since, L.H.S. = R.H.S. Hence, proved that sin(A - B) = sin A cos B - cos A sin B. (iv) To verify, tan (A - B) = . Substituting values in L.H.S. of equation : tan (A - B) = tan (60° - 30°) = tan 30° = . Substituting values in R.H.S. of equation : Since, L.H.S. = R.H.S. Hence, proved that tan (A - B) = .

Mathematics

If A = 60° and B = 30°, verify that (i) sin(A + B) = sin A cos B + cos A sin B (ii) cos(A + B) = cos A cos B - sin A sin B (iii) sin(A - B) = sin A cos B - cos A sin B (iv) tan(A - B) = tanA-tanB/1+tanAtanB

Trigonometrical Ratios

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