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A and B are positive acute angles Ifsin (A+B) = √3/2 and cos (A-B) = 1/√2,find values of A and B. |
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Answer» -step EXPLANATION:AnswerGiven sin(A+B)=1⇒sin(A+B)=sin90 o (∵sin90 o =1)⇒A+B=90 o …………(1)Again, cos(A−B)= 3 /2⇒cos(A−B)=cos30 o (∵cos30 o = 3 /2)⇒A−B=30 o …………(2)Adding (1)+(2)A+B+A−B=90 o +30 o ⇒2A=120 o ⇒A=120/2⇒A=60 o Putting A=60 o in EQUATION-(2) we getA−B=30 o ⇒60 o −B=30 o ⇒60 o −30 o =B⇒B=30 o ∴A=60 o ;B=30 |
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