Question

How I write this expression in terms of sines and/or cosines, and then simplify? 1+cosαtanαcscα/cscα

Answer 1

`1+sin alpha`

Explanation:

`1+cos alpha tan alpha csc alpha/csc alpha`

`1+(cos alpha × tan alpha × cancel(csc alpha))/ cancel(csc alpha)`

`1+ cos alpha × tan alpha color(blue)(rarr 1)`

`tan alpha= sin alpha/cos alpha color(blue)(rarr 2)`

Putting value of `tan alpha` from `color(blue)(2)` in `color(blue)(1)`

`1+ cos alpha × sin alpha/ cos alpha`

`1+ cancel(cos alpha) × sin alpha/ cancel(cos alpha)`

`1+ sin alpha`