CBSE Class 11-science Answered
trigonometry
Asked by ashwinivg | 25 Jun, 2010, 02:46: PM
Expert Answer
Dear student, following is the answer to your query:
6 cos θ + 8 sin θ = A sin(θ + α)
Using the result, sin(x+y) = sinx cosy + cosx siny, in RHS,
6 cos θ + 8 sin θ = A sin θ cos α + A sin α cos θ
Now comparing both sides we find,
6 = A sin α and 8 = A cos α
or sin α = 6/A and cos α = 8/A
Now squaring these results and adding them, we get:
sin2α + cos2α = 36/A2 + 64/A2
36/A2 + 64/A2 = 1
A2 = 100
A = ±10
Using the result, sin(x+y) = sinx cosy + cosx siny, in RHS,
6 cos θ + 8 sin θ = A sin θ cos α + A sin α cos θ
Now comparing both sides we find,
6 = A sin α and 8 = A cos α
or sin α = 6/A and cos α = 8/A
Now squaring these results and adding them, we get:
sin2α + cos2α = 36/A2 + 64/A2
36/A2 + 64/A2 = 1
A2 = 100
A = ±10
Regards
TopperLearning
Answered by | 14 Jul, 2010, 02:16: PM
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