If ${log}_{| s i n x |} | c o s x | + {log}_{| c o s x |} | s i n x | = 2$ then |tanx|

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Solution

The correct option is C
1

Here ${log}_{| s i n x |} | c o s x | + \frac{1}{{log}_{| s i n x |} | c o s x |} = 2$

$\Rightarrow y + \frac{1}{y} = 2$ Where y = ${log}_{| s i n x |} | c o s x |$

$\Rightarrow y = 1 \Rightarrow {log}_{| s i n x |} | c o s x |$

$\Rightarrow y = 1 \Rightarrow {log}_{| s i n x |} | c o s x |$ = 1

$\Rightarrow | s i n x | = | c o s x | \Rightarrow | t a n x | = 1$

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