tan2θ + cot2θ - sec2θ cosec2θ இன் மதிப்பு:

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)
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  1. 2
  2. -2
  3. 0
  4. 1/2

Answer (Detailed Solution Below)

Option 2 : -2
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கொடுக்கப்பட்டது:

tan2θ + cot2θ  - sec2θ cosec2θ
பயன்படுத்தப்பட்ட கருத்து:

1. tanα = sinα/cosα

2. cotα = 1/tanα

3. secα = 1/cosα

4. cosecα = 1/sinα

5. (a + b)2 - 2ab = a2 + b2

6. sin2α + cos2α = 1

கணக்கீடு:

tan2θ + cot2θ  - sec2θ cosec2θ

⇒ -2

∴ தேவையான பதில் -2.

Shortcut Trick 

இந்தக் கேள்வியைத் தீர்க்க மதிப்பு வைக்கும் முறையைப் பயன்படுத்தவும்,

θ = 45° ஐப் பயன்படுத்தவும்

tan2θ + cot2θ  - sec2θ cosec2θ
⇒ 12 + 12  - (√2)2(√2)2

⇒ 1 + 1 - 4

⇒ 2 - 4 = - 2

∴ இந்தக் கேள்விக்கான சரியான பதில் -2.

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