Question

Log_2[3.sin50/cos40+5.cosec40/sec50.cosec40]

Answer 1

Answer:

$\bold\red{Value = 3}$

Step-by-step explanation:

The correct Question is :-

$log_{2}(3 \times \frac{ \sin(50) }{ \cos(40) } + 5 \times \frac{ \csc(40) }{ \sec(50) } )$

Now, we know that,

sinß = cos (90-ß)

=> sin 50 = cos (90-50) = cos 40

and,

secß = cosec (90-ß)

=> sec 50 = cosec (90-50) = cosec 40

So, putting these values in given Question,

we get,

$= log_{2}(3 \times \frac{ \sin(50) }{ \sin(50) } + 5 \times \frac{ \sec(50) }{ \sec(50) } ) \\ \\ = log_{2}(3 \times 1 + 5 \times 1) \\ \\ = log_{2}(3 + 5) \\ \\ = log_{2}(8) \\ \\ = log_{2}( {2}^{3} ) \\ \\ = 3 \times log_{2}(2) \\ \\ = 3 \times 1 \\ \\ = 3$

Hence, the value of log is 3

Concepts Used :-

$(1) \: \: log_{a}( {b}^{m} ) = m \times log_{a}(b) \\ \\ (2) \: \: log_{a}(a) \: = 1$