that sinα=1/3 andcosβ=1/2 what is the value of (α+β)
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Let, (a+b)= k
=>sin(a+b) = sin(k)
=>sin(a)cos(b) + sin(b)cos(a) = sin(k)
=>(1/3)(1/2) + (√1-(1/2)²)(√1-(1/3)²) = sin(k)
=>1/6 + (√3/2)(2√2/3) = sin(k)
=>(1+2√6)/6 = sin(k)
=>sin(k) = 0.983
=>k = 79.42°/ 1.386 radians
therefore,
a+b = 79.42°/ 1.386 radians
=>sin(a+b) = sin(k)
=>sin(a)cos(b) + sin(b)cos(a) = sin(k)
=>(1/3)(1/2) + (√1-(1/2)²)(√1-(1/3)²) = sin(k)
=>1/6 + (√3/2)(2√2/3) = sin(k)
=>(1+2√6)/6 = sin(k)
=>sin(k) = 0.983
=>k = 79.42°/ 1.386 radians
therefore,
a+b = 79.42°/ 1.386 radians
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