tan2 θ + cot2 θ - sec2θ cosec2 θ याचे मूल्य किती आहे?

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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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दिलेल्याप्रमाणे:

tan2θ + cot2θ  - sec2θ cosec2θ
वापरलेली संकल्पना:

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

गणना:

tan2θ + cot2θ  - sec2θ cosec2θ

\(\frac {sin^2θ}{cos^2θ} + \frac {cos^2θ}{sin^2θ} - \frac {1}{sin^2θ \times cos^2θ}\)

\(\frac {sin^4θ + cos^4θ - 1}{sin^2θ \times cos^2θ}\)

\(\frac {(sin^2θ + cos^2θ)^2 - 2sin^2θ cos^2θ - 1}{sin^2θ \times cos^2θ}\)

\(\frac {(1)^2 - 2sin^2θ cos^2θ - 1}{sin^2θ \times cos^2θ}\)

\(\frac {-2sin^2θ cos^2θ}{sin^2θ \times cos^2θ}\)

⇒ -2

∴ आवश्यक उत्तर -2 आहे.

Shortcut Trick 

हा प्रश्न सोडवण्यासाठी मूल्य पुटिंग पद्धत वापरा,

θ = 45° वापरा
Trigo

tan2θ + cot2θ  - sec2θ cosec2θ

⇒ 12 + 12  - (√2)2(√2)2

⇒ 1 + 1 - 4

⇒ 2 - 4 = - 2

∴ या प्रश्नाचे योग्य उत्तर -2 आहे.

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