3 + tan2θ + cot2θ − sec2θ cosec2θ का मान है:

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Option 4 : 1
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दिया गया है:

व्यंजक: 3 + tan2θ + cot2θ − sec2θ × cosec2θ

प्रयुक्त सूत्र:

tan2θ = sec2θ − 1

cot2θ = cosec2θ − 1

गणना:

⇒ 3 + (sec2θ − 1) + (cosec2θ − 1) − sec2θ × cosec2θ

⇒ 3 + sec2θ + cosec2θ − 2 − sec2θ × cosec2θ

⇒ (1 + sec2θ + cosec2θ − sec2θ × cosec2θ)

अब θ = 45° मानकर सरल करते हैं (एक मान्य सर्वसमिका कोण जहाँ सभी मान परिभाषित हैं)

⇒ sec 45° = √2, इसलिए sec2θ = 2

⇒ cosec 45° = √2, इसलिए cosec2θ = 2

⇒ व्यंजक = 1 + 2 + 2 − (2 × 2)

⇒ 1 + 4 − 4 = 1

इसलिए, व्यंजक का मान 1 है।

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