What do the symbols like log ,abs,hyp,sin,cos,tan,rcl,m+ ang eng stand for

You sure will benefit more from your calculator by taking a look at its manual. After all that is what it was created for.

No matter. I am willing to presume that if you are asking about these keys that is because you have not seen the relevant functions yet in your Math courses. One day or another (soon) you will know about them, and I will not go into explaining what they are or what they are used for. (Awfully SORRY)

1. ENG signifies engineering notation (No I will not explain what it is).
   
2. SIN, COS, and TAN are the keys for the trigonometric function sine, cosine, and tangent.
3. HYP is entered before a trigonometric function key to calculate its hyperbolic counterpart : the hyperbolic sine (HYP SIN), the hyperbolic cosine (HYP COS), and the hyperbolic tangent (HYP TAN).
4. RCL followed by a letter recalls a value stored in memories, A, B, C, D, M.
5. ABS takes the absolute value of an expression.
6. IN, I do not know, but it might be LN for natural logarithm.
   

The FX-115ES is somewhat different to other calculators you might know. The sequence of keys is more like writing up a calculation in a textbook, whereas for "normal" calculators operations are reversed in some places.
For example, with most calculators you would type 30 [sin] to calculate the sine function of 30 degrees, with the 115ES its [sin] 30 [=].

The 115ES has all the standard trigonometric functions:

• Standard functions (sin, cos, tan), type the [sin], [cos] or [tan] key followed by the argument.
• Inverse trigonometric (sin?¹, cos?¹, tan?¹), type [SHIFT][sin], [SHIFT][cos] or [SHIFT][tan] followed by the argument.
• Hyperbolic functions (sinh, cosh, tanh), type [HYP][sin], [HYP][cos], or [HYP][tan] followed by the argument.
• and finally inverse hyperbolic (sinh?¹, cosh?¹, tanh?¹), its [SHIFT][HYP][sin], [SHIFT][HYP][cos], or [SHIFT][HYP][tan] followed by the argument.

Arguments can be given as numbers with mantissa (2.718), as fractions (use the fraction key below [CALC]) or as degree, minute, second (30°12'45") using the [°'"] key for input. To switch between degrees (1 circle = 360°), radians (1 circle = 2?), or grad (1 circle = 400 gon), use [SHIFT][DRG>].

The hyp key is used with the cos, sin, and tan keys to compute the hyperbolic cosine, hyperbolic sine, and hyperbolic tangent functions (and their inverses).

The hyperbolic functions are computed the same way as the trignometric functions: simply press the hyp key just before pressing the desired trig key.

No solution, but I have the exact same problem with a Sharp EL-531W calculator. Doesn't matter whether mode is degrees, radians, etc., and resetting with button in back has no effect.

No post is an adequate substitute for reading the manual. Here is the meaning of some of the primary keys.

1. hyp.: To calculate hyperbolic functions: hyp + sin calculates the hyperbolic sine, hyp + cos calculates the hyperbolic cosine, hyp + tan calculates the hyperbolic tangent (sinh, cosh, tanh)
2. sin. To calculate the sine of an angle
3. cos.To calculate the cosine of an angle
4. tan. To calculate the tangent of an angle
5. yx : y with raised x, calculates general powers
6. ln: calculates the natural logarithm (log in base e)
7. log: calculates the logarithm in base 10
8. ab/c : used to enter mixed fractions; 13 ab/c 7 ab/c 5 enter the mixed fraction 13 and 7/5
9. x10 to the X : calculates the exponential function on some calculators. used to enter powers of 10 as in scientific notation; 6.02x10^23 is keyed in as 6.02 EXP 23 (Avogadro's Number of Chemistry and Physics)
10. (-).: This is the change sign. It negates the value of a number. If a result is positive it makes it negative, and if it is negative it makes positive
11. deg ' " : used to convert between decimal degrees and degree, minute, second.
    
12. rcl : used In conjunction with a memory location, recalls the contents of the memory ( if there is one memory M, extracts what is in M and displays it)
13. sto: used in conjunction with the name of a memory register, stores a result or an entry in the relevant memory.
14. M+ adds the content of the display to the constant memory M

108/(138.8*1000)

You should buy a dog that takes you on walks.
Then you won't have the problem that you have.

I shall attempt :D
1) cosec A + cot A = 3
we know that (cot A)^2 + 1 = (cosec A)^2
Hence, (cosec A)^2 - (cot A)^2 = 1
thus, (cosec A + cot A) (cosec A - cot A) = 1
3 (cosec A - cot A) = 1
(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3
(cosec A + cot A) = 3
Summing them, 2 cosec A = 3 1/3
cosec A = 6 2/3 = 5/3
sin A = 0.15
Thus, cos A = sqrt (1 - (sin A)^2) = 0.989


2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2
expand
LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x
We can calculate that
tan x cosec x = sec x (since tan x = sin x / cos x)
sec x cot x = cosec x
so the above is
LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x
LHS = 2 + cot x + tan x - sec x cosec x
LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)
LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)
LHS = 2 (proved)

for function = (sin,cos,tan,sec,cosec,cotan)
arc(function) = function^-1, calculated in the first quadrant for simplicity(0-pi/2) (0-90deg), as all functions repeat circularly
just another method of notation

http://www.mathwords.com/t/tangent_inverse.htm