Question

If tanθ=1/√2, find the value of cosec²θ-sec²θ/cosec²θ+cot²θ

Answer 1

Answer:

3 / 10

Step-by-step explanation:

Given :

tan Ф = 1 / √ 2

We have to find value of :

cosec² Ф - sec² Ф / cosec² Ф + cot² Ф

We know :

tan Ф = P / B

Also :

H² = P² + B²

H = √ P² + B²

H = √ 1 + 2

H = √ 3

Now we have :

H = √ 3 , P = 1 and B = √ 2

cosec² Ф - sec² Ф / cosec² Ф + cot² Ф

= > [ ( H / P )² - ( H / B )² ] / [ ( H / P )² + ( B / P )² ]

Putting values here we get :

= > ( 3 / 1 - 3 / 2 ) / ( 3 / 1 + 2 / 1 )

= > ( 3 / 2 ) / ( 5 / 1 )

= > ( 3 / 10 )

Therefore , the value of cosec² Ф - sec² Ф / cosec² Ф + cot² Ф is 3 / 10 .

Answer 2

Answer:

$\frac{3}{10}$

Step-by-step explanation:

Given Tan θ = 1/√2

We know that Tan θ = p/b

So, p= 1 and b= √2 , We have to find h

Also we know that H²= P²+b²

So, H² = (1)² + (√2)²

= √1 + 2

H² = √3

So now we have all values p= 1 , b= √2 and h= √3

To find :- cosec²θ-sec²θ/cosec²θ+cot²θ

• Cosecθ = h/p = √3/1
• Secθ= h/b = √3/√2
• Cotθ= b/p= √2/1

Putting these values in the given equation ↓

$\large\implies{\sf }$(√3)² – (√3/√2)² / (√3)² + (√2/1)²

$\large\implies{\sf }$3 – (3/2) / 3 + (2/1)

$\large\implies{\sf }$ 3/2 x 1/5 = 3/10