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Question

If 0<x<π2 and cosx=310, then the value of log10sinx+log10cosx+log10tanx is equal to

A
0
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B
1
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C
1
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D
none of these
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Solution

The correct option is C 1
Given that, 0<x<π2 and cosx=310
Let, a=log10sinx+log10cosx+log10tanx
a=log10(sinxcosxtanx)[loga+logb+logc=log(abc)]
=log10sin2x
=log10(1cos2x)
a=log101(310)2=log10101=1log1010=1,[logaa=1]
Ans: C

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