If sin(x)=1/2, then solve trignometric expression cos(x)csc(x) calculator

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Solution

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2. Find the value of other five trigonometric functions or solve expression

1. If `sin(x)=5/13` then find values of other trigonometric functions

2. If `cos(x)=12/13` then find values of other trigonometric functions

3. If `tan(x)=5/12` then find values of other trigonometric functions

4. If `csc(x)=13/5` then find values of other trigonometric functions

5. If `sec(x)=13/12` then find values of other trigonometric functions

6. If `cot(x)=12/5` then find values of other trigonometric functions

1. If `sin(x)=3/5` then solve `cos(x)csc(x)+tan(x)sec(x)`

2. If `tan(x)=1/2` then solve `(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))`

3. If `sin(x)=4/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`

4. If `cos(x)=3/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`

Example

1. If `sin(x)=3/5`, solve `cos(x)csc(x)+tan(x)sec(x)`

Solution:
`sin(x)=3/5` (given)

`cos(x)csc(x)+tan(x)sec(x)=?`

`sin(x)=3/5`, in Quadrant-1

`(1)` `cos^2(x)=1-sin^2(x)`

`=1-(3/5)^2`

`=1-9/25`

`=(25-9)/25`

`=16/25`

`:.cos(x)=sqrt(16/25)=4/5=4/5`

`(2)` `tan(x)=sin(x)/cos(x)=(3/5)/(4/5)=3/5 xx 5/4=3/4=3/4`

`(3)` `csc(x)=1/sin(x)=1/(3/5)=5/3=5/3`

`(4)` `sec(x)=1/cos(x)=1/(4/5)=5/4=5/4`

Now substitute all these expression values in
`cos(x)csc(x)+tan(x)sec(x)`

`=(4/5)(5/3)+(3/4)(5/4)`

`=4/3+15/16`

`=109/48`

`:. cos(x)csc(x)+tan(x)sec(x)=109/48`

Input functions

Sr No.	Function	Input value
1.	`x^3`	x^3
2.	`sqrt(x)`	sqrt(x)
3.	`root(3)(x)`	root(3,x)
4.	sin(x)	sin(x)
5.	cos(x)	cos(x)
6.	tan(x)	tan(x)
7.	sec(x)	sec(x)
8.	cosec(x)	csc(x)
9.	cot(x)	cot(x)
10.	`sin^(-1)(x)`	asin(x)
11.	`cos^(-1)(x)`	acos(x)
12.	`tan^(-1)(x)`	atan(x)
13.	`sin^2(x)`	sin^2(x)
14.	`log_y(x)`	log(y,x)
15.	`log_10(x)`	log(x)
16.	`log_e(x)`	ln(x)
17.	`e^x`	exp(x) or e^x
18.	`e^(2x)`	exp(2x) or e^(2x)
19.	`oo`	inf