Total number of values in -2 - 2 - and satisfying log -cos x-sin x-log -sin x-cos x-2 is

The correct option is D 8 log_|cosx||sinx|+log_|sinx||cosx|=2 i.e |sinx|=|cosx|≠ 1 and |tanx|=1 ∴ x=±π/4, ± ( π π/4 ), ± ( π+π/4 ), ± ( 2 π π/4 ) i.e 8 ...

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Standard XI

Mathematics

Trigonometric Equations

Total number ...

Question

Total number of values in $(- 2 π, 2 π)$ and satisfying
$l o g_{| c o s x |} | s i n x | + l o g_{| s i n x |} | c o s x | = 2$ is

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Solution

The correct option is D
8

$l o g_{| c o s x |} | s i n x | + l o g_{| s i n x |} | c o s x | = 2 i . e | s i n x | = | c o s x | \neq 1 a n d | t a n x | = 1 ∴ x = \pm \frac{π}{4}, \pm (π - \frac{π}{4}), \pm (π + \frac{π}{4}), \pm (2 π - \frac{π}{4}) i . e 8 v a l u e s .$

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Similar questions

Total number of values in $(- 2 π, 2 π)$ and satisfying
$l o g_{| c o s x |} | s i n x | + l o g_{| s i n x |} | c o s x | = 2$ is

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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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_______

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Total number of values in (−2π,2π) and satisfying log|cosx||sinx|+log|sinx||cosx|=2 is

The correct option is D 8 log|cosx||sinx|+log|sinx||cosx|=2i.e |sinx|=|cosx|≠1 and |tanx|=1∴x=±π4, ±(π−π4), ±(π+π4), ±(2π−π4) i.e 8 values.

Total number of values in $(- 2 π, 2 π)$ and satisfying
$l o g_{| c o s x |} | s i n x | + l o g_{| s i n x |} | c o s x | = 2$ is

The correct option is D
8

$l o g_{| c o s x |} | s i n x | + l o g_{| s i n x |} | c o s x | = 2 i . e | s i n x | = | c o s x | \neq 1 a n d | t a n x | = 1 ∴ x = \pm \frac{π}{4}, \pm (π - \frac{π}{4}), \pm (π + \frac{π}{4}), \pm (2 π - \frac{π}{4}) i . e 8 v a l u e s .$