Question

What is the value of $\frac{tan^{2} \Theta-sec^{2} \Theta}{cot^{2} \Theta-cosec^{2} \Theta}$.

Answer 1

Answer:

The value of (tan² θ −  sec² θ)/(cot² θ −  cosec² θ) is 1.

Step-by-step explanation:

Given : (tan² θ −  sec² θ)/(cot² θ −  cosec² θ)

(tan² θ −  sec² θ)/(cot² θ −  cosec² θ)

= -1 (sec² θ - tan² θ) / -1 (cosec² θ - cot² θ)

= (sec² θ - tan² θ) / (cosec² θ - cot² θ)

= 1/1

[By using  an identity, sec² θ -  tan² θ =  1 & cosec² θ - cot² θ = 1 ]

= 1

(tan² θ −  sec² θ)/(cot² θ −  cosec² θ) = 1

Hence, the value of (tan² θ −  sec² θ)/(cot² θ −  cosec² θ) is 1.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

According to the Question:

Refer to the attachment for step-by-step-explanation with answer.

⇒(tan² θ − sec² θ)/(cot² θ − cosec² θ) = 1

Hence Proved ! __________[ANSWER]