Question

if cosec@=2/3 find the value of cot^2@-2cot@+1​

Answer 1

Answer:

17/8

Step-by-step explanation:

cosecθ−cotθ=2⟶(1)

Now, (cosec 2 θ−cot 2 θ)=1

⇒(cosecθ−cotθ)(cosecθ+cotθ)=1

⇒2(cosecθ+cotθ)=1

⇒(cosecθ+cotθ)= 21 ⟶(2)

Adding (1)&(2), we get

⇒2cosecθ=2+ 21= 25

⇒cosecθ= 45

⇒cosec 2 θ= 1625

Again (2)−(1), we get

⇒2cotθ= 21 −2=− 23

⇒cotθ=− 43

⇒cot 2 θ= 169

⇒cosec 2 θ+cot 2 θ= 1634= 817