Question

9. Given that sin a = 1/2 and cos B = 1/2, then the value of (a+b) is
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Answer 1

Answer:

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Step-by-step explanation:

cosA+cosB=12⟹2cos(A+B2)cos(A−B2)=12(1)

sinA+sinB=14⟹2sin(A+B2)cos(A−B2)=14(2)

dividing (2) by (1)

tan(A+B2)=12

⟹tan2(A+B2)=14

⟹sec2(A+B2)−1=14

⟹sec2(A+B2)=1+14=54

⟹cos2(A+B2)=45

⟹2cos2(A+B2)=85

⟹2cos2(A+B2)−1=85−1=35

⟹cos(A+B)=35∵2cos2θ−1=cos2θ

Q.E.D