Prove: -
cot+cosec-1 upon cot-cosec+1 is equal to cosec + cot
Answers
Answer:
solved
Step-by-step explanation:
coxt+cosecx-1 upon cotx-cosecx+1 = cotx+cosecx-1 ÷ cotx-cosexc+1
= 1 +cotx - secx ÷ 1 +cotx - cosecx
= (1 +cotx - secx)( 1 +cotx + cosecx ) ÷ (1 +cotx - cosecx)( 1 +cotx + cosecx )
= (1 +cotx - secx)( 1 +cotx + cosecx ) ÷ (1 +cotx )² - cosec²x
= (1 +cotx - secx)( 1 +cotx + cosecx ) ÷ (1 +cotx )² - cosec²x
= (1 +cotx - secx)( 1 +cotx + cosecx ) ÷ (1 +2cotx - 1)
= (1 +cotx - secx)( 1 +cotx + cosecx ) ÷ 2cotx
= (1 +cotx )² - (1 +cotx ) (cosec x - secx) - cosecx secx ÷ 2cotx
= 1 + 2cotx + cot²x - (1 +cotx ) (cosec x - secx) - cosecx secx ÷ 2cotx
= 2cotx + cosec²x - (1 +cotx ) (cosec x - secx) - cosecx secx ÷ 2cotx
= 2cotx + cosec²x - cosec x + secx - cotx cosecx + cotx secx - cosecx secx ÷ 2cotx
= 2 + cosec²x tanx - cosec xtanx + secxtanx - cosecx + secx - sec²x ÷ 2
= 2 + cosec²x tanx - cosec xtanx + secxtanx - cosecx + secx - sec²x ÷ 2
= cosec x + cotx