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Question

If tan θ=32, the sum of the infinite series 1 + 2 (1cos θ)+3(1cos θ)2+4(1cos θ)3+.... is

A
23
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B
34
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C
522
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D
52
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Solution

The correct option is D 52
1+2x+3x2+4x3++(r+1)xr+.....to =(1x)2, [let (1cos θ)=x] series=(11+cos θ)2=sec2 θ=(1+tan2 θ)=1+32=52

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