Question

Topic trigonometry (4)
please answer ASAP​

Answer 1

Step-by-step explanation:

please see the answer in attachment.

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Answer 2

$\bigstar \sf \large \bf \underline{\underline{Given:-}}$

• $\sf tan \theta = \frac{1}{\sqrt{3} }$

$\bigstar \sf \large \bf \underline{\underline{To \ find:-}}$

• $\sf Value \ of \ \frac{cosec^2 \theta - sec^2 \theta}{cosec^2\theta+ sec^2 \theta}$

$\bigstar \sf \large \bf \underline{\underline{Solution:-}}$

From the trignometric table ,

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❥ tan 30°= 1/√3.

❥  Cosec 30° = 2

❥ Sec 30° = 2/√3.

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Given that , tan θ = 1/√3

   ∴ θ = 30°

Now ,

$\implies \sf \frac{cosec^2 \theta - sec^2 \theta}{cosec^2\theta + sec^2 \theta}$

Substituiting the value of 'θ' in this eqn,

$\implies \sf \frac{cosec^2 30 - sec^2 30}{cosec^2 30+ sec^2 30}$

$\implies \sf \frac{2^2 - (2/ \sqrt{3})^2 }{2^2 +(2/ \sqrt{3})^2 } \\\\\\\implies \sf \frac{4 - 4/3}{4+4/3} = \frac{12-4 / 3 }{12+4/ 3}\\\\\\\implies \sf \frac{ 12 - 4}{12+4} = 8 / 16 \\\\\\\implies \sf 2/4 \\\\\\\implies \boxed{1/2.}$

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