Question

1. Prove by vector method that sin(a + B) = sina cosß + cosa sinß. ​

Answer 1

▬▬Prove by vector method that sin(a + B) = sina cosß + cosa sinß✯▬▬

↪Here, vector OP = ai + bj and vector OQ = ci + dj

↪Now, OP × OQ = (ad – bc)k

[(OP)(OQ)sin(∠POQ)] ↪= (ad – bc)k –sin(A – B)

↪= (ad – bc)/(OP)(OQ)

↪ = (a/OP).(d/OQ).(b/OP).(c/OQ)

↪ = cosA.sinB – sinA.cosB sin(A – B)

↪= sinA.cosB – cosA.sinb

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