Question

prove that 1 + Cot ²theta = cosec²theta ​

Answer 1

Answer:

cosec^2-cot^2=1

cosec theta=hypotenuse/opposite=ac/ab

cot theta=adjacent/opposite=bc/ab

Step-by-step explanation:

by pythagoreas theorem. (ac)^2=(ab)^2+(bc)^2

taking (ab)^2 on both sides for dividing

(ac)^2/(ab)^2=(ab)^2/(ab)^2+(bc)^2/(ab)^2

[in r.h.s ab^2 and ab^2 are cancelled]

(ac/ab)^2=(1)^2 (bc/ab)^2

then {we consider that ac/ab=cosec theta and bc/ab=cot theta}

therefore (cosec theta)^2=(1)^2+(cot theta)^2

hence proved