Question

What is the value of tan²θ-sec²θ/cot²θ-cosec²θ?

Answer 1

Answer:

1

Step-by-step explanation:

Given : ${\sf{\ \ {\dfrac{tan^2 \theta - sec^2 \theta}{cot^2 \theta - cosec^2 \theta}}}}$

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• ${\boxed{\sf{\gray{1 + tan^2 \theta = sec^2 \theta}}}}$

${\sf{\gray{From \ this, \ we \ get \ [ tan^2 \theta - sec^2 \theta = - 1]}}}$

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• ${\boxed{\sf{\gray{1 + cot^2 \theta = cosec^2 \theta}}}}$

${\sf{\gray{From \ this, \ we \ get \ [ cot^2 \theta - cosec^2 \theta = - 1]}}}$

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Putting known values, we get

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$\Rightarrow{\sf{ {\dfrac{- 1}{- 1}} }}$

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$\Rightarrow{\boxed{\sf{\red{1}}}}$

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Other identities which are frequently used :

• sin²θ + cos²θ = 1

• sin θ = P/H = 1/cosec θ

• cos θ = B/H = 1/sec θ

• tan θ = P/B = 1/cot θ

Answer 2

$\huge\bold\green{Question}$

What is the value of

tan²θ-sec²θ / cot²θ-cosec²θ ?

$\huge\bold\green{AnsWer}$

Given : →

$\implies{\tt{\ \ {\dfrac{tan^2 \theta - sec^2 \theta}{cot^2 \theta - cosec^2 \theta}}}}$

$\implies\tt{1 + tan^2 \theta = sec^2 \theta}$

From the above-mentioned value , we get →

$\implies\tt{ [ tan^2 \theta - sec^2 \theta = - 1]}$

$\implies\tt{1 + cot^2 \theta = cosec^2 \theta}$

From the above-mentioned value , we get →

$\implies\tt{ [ cot^2 \theta - cosec^2 \theta = - 1]}$

By substituting the values we get →

→ ${\tt{ {\dfrac{- 1}{- 1}} }}$

→ $\huge\bold\blue{1}$