Question

Evaluate cosec (75+theta) - sec (15-theta) - tan (55+theta) + cot (35- theta )​

Answer 1

Answer:

Step-by-step explanation:

cosec (75+θ) - sec (15-θ) - tan (55+θ) + cot (35- θ)​

First let us convert into simpler numbers

Cosec(75 + θ ) = Cosec ( 90-(15 - θ)) = Sec(15 - θ) (∵ Cosec (90 - Φ) = SecΦ)

Tan(55+θ)  = Tan( 90 - (35 - θ)) = Cot(35 - θ)         (∵ Tan (90 - Φ) = CotΦ)

Now substitute the values in given equation,

cosec (75+θ) - sec (15-θ) - tan (55+θ) + cot (35- θ)​

=> Sec(15 - θ) - Sec(15 - θ) - Cot(35 - θ) + Cot(35 - θ)

=> 0 - 0

=> 0

Answer 2

Refer attachment for a answer...

it's looks long because I solved it step by step