Question

Tan theta minus cot theta equals 2sin square theta minus 1 upon sin theta cos theta.

Answer 1

Step-by-step explanation:

LHS : tan∆ - cot ∆

= sin∆ / cos∆ - cos∆ / sin∆

taking LCM

= sin²∆ -cos²∆

sin∆.cos∆

= sin²∆ - (1-sin²∆)

sin∆.cos∆. ........(cos²∆ = 1-sin²∆)

= sin²∆ + sin²∆ -1

sin∆.cos∆

= 2sin²∆ -1

sin∆.cos∆. ...........(Hence Proved)

therefore

tan∆ - cot ∆ = 2sin²∆ -1

sin∆.cos∆.

hence Proved