Question

find the value of ( cosec square theta - 1 ) tan squars theta

Answer 1

hi!

i will be using A instead of theta

we have ,

(cosec²A-1)tan²A

=> cot²Atan²A [ since cosec²A=1+cot²A]

=> (1/tan²A)(tan²A) [since cotA=1/tanA]

=> 1 [canceled out tan²A]

Answer 2

The value of ($cosec^{2}$θ-1)$tan^{2}$θ is 1

Given:

($cosec^{2}$θ-1)$tan^{2}$θ

We need to find the value of ($cosec^{2}$θ-1)$tan^{2}$θ

Putting the value of $cosec^{2}$θ=1+$cot^{2}$θ, we will get

(1+$cot^{2}$θ-1)  $tan^{2}$θ

$cot^{2}$θ×$tan^{2}$θ

Now, we will put the value of $cot^{2}$θ= $\frac{1}{tan^{2}θ }$

$\frac{1}{tan^{2}θ}$×$tan^{2}$θ

= 1

Thus, the value of ($cosec^{2}$θ-1)$tan^{2}$θ is 1.

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