Question

tan^2theta×cosectheta-1/1+costheta+cosec^2theta×costheta-1/1+cosectheta=0​

Answer 1

Answer

Explanation

cosec a -1 cos a - 1

tan²a × ________ + cosec²a × _______

1 + cos a cosec a + 1

1 cosec a -1 1 cos a - 1

= __ × _________ +____ × _______

cot²a 1 + cos a sin²a cosec a + 1

{ tan²a = 1/ cot²a , cosec²a = 1/sin²a }

cosec a -1 cos a - 1

= ___________ + ___________

(cosec²a -1)(1 +cos a) (1- cos²a)(cosec a +1)

{cosec²a - cot²a =1 -> cosec²a -1 = cot²a}

{ sin²a + cos²a =1 -> sin²a = 1 - cos²a }

cosec a -1 cos a - 1

= ___________________ + _________

(coseca-1)(coseca+1)(1+cosa) (1-cosa(1+cosa)

(coseca+1)

{a² - b² = (a-b)(a+b) }

1 (-1)

= _____________+ _______________

(cosec a+1)(1+cos a) (1+cos a)(coseca+1)

1 1

= _____________ - _______________

(cosec a+1)(1+cos a) (1+cos a)(coseca+1)

= 0

Hence proved

Hope the explanation is clear....