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Question

If 3sinθ+4cosθ=5, then the value of sinθ is


A

23

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B

45

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C

35

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D

53

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Solution

The correct option is C

35


Given, 3sinθ+4cosθ=5.......(1)Squaring both sides, we have:(3sinθ+4cosθ)2=(5)29sin2θ+16cos2θ+24sinθcosθ=259(1cos2θ)+16(1sin2θ)+24sinθcosθ=2599cos2θ+1616sin2θ+24sinθcosθ=2516sin2θ+9cos2θ24sinθcosθ=0(4sinθ3cosθ)2=04sinθ3cosθ=0......(2)Solving (1) and (2),sinθ=35


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