Value of `(3+cot80^0cot20^0)/(cot80^0+cot20^0)` is equal to (a)`cot20^0` (b) `tan50^0` (c)`cot50^0` (d) `cotsqrt(20^0)`

Explanation

`(3+cot80^@cot20^@)/(cot80^@+cot20^@)`

`=(3+(cos80^@/sin80^@ )(cos20^@/sin20^@))/((cos80^@/sin80^@)+(cos20^@/sin20^@))`

`=(3sin80^@sin20^@+cos80^@cos20^@)/(sin20^@cos80^@+sin80^@cos20^@)`

`=(2sin80^@sin20^@+cos(80^@-20^@))/(sin(20^@+80^@)`

`=(cos60^@ - cos100^@ +cos60^@)/(sin100^@)`

`=(2cos60^@ - cos100^@ )/(sin100^@)`

`=(2(1/2) - cos100^@ )/(sin100^@)`

`=(1 - cos100^@ )/(sin100^@)`

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