Question

log sin tita+log cosec tita=

Answer 1

log sin x+log cosec x
we know,loga +log b=log ab
⇒log sin x+log cosec x =log sinx*cosecx
                                      = log 1  [∵sin x * cosec x=1]
                                      = 0
∴log sin x+ log cosec x = 0 

Answer 2

Question: log(sin$\theta$) + log(cosec$\theta$) =

Answer:

The value of logarithm function log(sin$\theta$) + log(cosec$\theta$) is 0.

Step-by-step explanation:

Some properties of the logarithm function:-

(i) log a $+$ log b $=$ log(ab)

(ii) log a - log b = log($\frac{a}{b}$)

(iii) alog b = log($b^a$)

(iv) log1 = 0

(v) log($10^n$) = $n$

Step 1 of 1

Consider the given logarithm function as follows:

log(sin$\theta$) + log(cosec$\theta$)

Using the property (i) of logarithm function, we have

log(sin$\theta$ cosec$\theta$) _____ (1)

As we know,

cosec$\theta$ = 1/sin$\theta$

So, substitute the value of cosec$\theta$ in the function (1) as follows:

⇒ log(sin$\theta$ × 1/sin$\theta$)

⇒ log(1)

⇒ 0 (Since log1 = 0)

Therefore, the value of given logarithm function is 0.

#SPJ3