Algebra and Trig questions?

Question

Need help with these questions. Each question is either true or false. If true just say true, if false the answer must be corrected. Here's an example.

(a + b) / (c + d) = a /c + b / d That is false the correct answer is a/(c + d) = b/(c + d). if you could answer them in this format it would be great. So here they are

1. If log( a ) =b, then a = b / log

2. If sin(a) = b, then a = b / sin

3. If cos(a) = b, then a = b / cos

4. If tan(a) = b, then a = b / tan

5. (Sin 2a) / a = sin (2)

6. 3/a + 3/b = 3 / (a+b)

7. a / (b+c) = a / b + a / c

Thanks for the help person with most answers will get best answer

Answer 1

I don't think any of them are right.

They have to do with inverse functions and you cannot divide by the function name.

I will do 1)

1)   log(a) = b then a = 10^b

This assumes that the log is base 10

2) if sin(a) = b then a = sin-1(b)  where sin-1 is the inverse sine not 1/sin.

etc.