Question

prove that please give me the answer

Answer 1

hope it will help you

Answer 2

Answer:

Every trigonometric function and its "co" version are related by:

fun θ = cofun ( 90° - θ )     and    cofun θ = fun ( 90° - θ )

(iii)

cos 20° = sin ( 90° - 20° ) = sin 70°      ----  so the first term is 1

cosec 20° = sec ( 90° - 20° ) = sec 70°    ---- so the second term is 1

cosec 20° = sec 70° = 1 / cos 70°     ---- so the third term is -2

The sum is then 1 + 1 - 2 = 0.

(iv)

cos 80° = sin ( 90° - 80° ) = sin 10°    ---- so the first term is 1

cosec 31° = sec ( 90° - 31° ) = sec 59° = 1 / cos 59°  --- so the second term is 1

The sum is then 1 + 1 = 2.