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kati45 [8]
2 years ago
5

Prove that 1/sin^2A -1/tan^2A= 1

Mathematics
1 answer:
Vika [28.1K]2 years ago
4 0

Answer:

Step-by-step explanation:

LHS =\dfrac{1}{Sin^{2} \ A }-\dfrac{1}{Tan^{2} \ A }\\\\\\ = \dfrac{1}{sin^{2} \ A}- \dfrac{1}{\dfrac{Sin^{2} \ A}{Cos^{2} \ A}}\\\\\\= \dfrac{1}{sin^{2} \ A } - \dfrac{Cos^{2} \ A}{Sin^{2} \ A}\\\\\\= \dfrac{1-Cos^{2} \ A}{Sin^{2} \ A}\\\\\\= \dfrac{Sin^{2} \ A}{Sin^{2} \ A}\\\\\\= 1 = \ RHS

Hint: 1 - Cos² A = Sin² A

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Answer:

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Step-by-step explanation:

From the  question we are told that  

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The probability that the  computer chip is not manufactured by company A and does not survive more than 500 temperature cycles is mathematically evaluated as

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Where B' \ and \   A' are a A and B complements and  | represented AND operator  

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        P(B' n A ' ) = [1 -  P (B' | A )] [1 - P(B )]

substituting values

         P(B' n A ' ) = [1 -  0.73] [1 - 0.42 ]

        P(B' n A ' ) = (0.27 )(0.58)

        P(B' n A ' ) =0.16

        P(B' n A ' ) =  16%

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