Question

COSEC A+COT A = 11/2 THEN TAN A

Answer 1

`\boxed{{\csc}^(2)\theta-{\cot}^(2)\theta=1}`

A trigonometric identity.

`\boxed{{a}^(2)-{b}^(2)=(a+b)(a-b)}`

An algebraic identity.

`\because{\csc}^(2)\theta-{\cot}^(2)\theta=1`

`\because{a}^(2)-{b}^(2)=(a+b)(a-b)`

`(11)/(2)(\csc A-\cot A)=1\implies\csc A-\cot A=(2)/(11)`

`2\cot A=(\csc A+\cot A)-(\csc A-\cot A)`

`2\cot A=(11)/(2)-(2)/(11)=(117)/(22)\implies \cot A=(117)/(44)\implies \tan A=(44)/(117)`