Question
Download Solution PDFtan2 θ + cot2 θ - sec2θ cosec2 θ याचे मूल्य किती आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्याप्रमाणे:
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
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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