Question

If cot theta =p+1/p prove that cosec theta+ cot theta= 2p or 1/2p

Answer 1

Answer:

Step-by-step explanation:

cot A =p+1/p                    .....(i)

cot²A =(p+1/p)²

cot²A =(p+1/p)²

cosec²A -1 =(p+1/p)²

cosec²A =  (p+1/p)² +1

cosec A = √[(p+1/p)² +1]          .....(ii)

adding (i) and (ii)

cot A + cosec A = p+1/p + √[(p+1/p)² +1]

cot A + cosec A =p+1/p + √[p²-2 + 1/p² - 1]

cot A + cosec A = [p²+1]/p + √[(p∧4 - 3p² +1 )/p²]

cot A + cosec A = [p²+1 + √(p∧4 - 3p² +1 )]/p

cot A + cosec A = [p²+1 ± (p² - 1)]/p

cot A + cosec A = [p²+1+p²-1]/p   ,   [p²+1-p²+1]/p}

cot A + cosec A = 2p   ,    1/2p