If cos^2A- sin^2A=tan^2B ,prove that tan^2A =cos^2B-sin^2B

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cos²A - sin²A = tan²B , then prove , cos²B - sin²B = tan²A

Given, cos²A - sin²A = tan²B

⇒cos²A - ( 1 - cos²A ) = tan²B [∵ sin²Ф = 1 - cos²Ф ]

⇒ cos²A - 1 + cos²A = tan²B

⇒ 2cos²A - 1 = tan²B

⇒ 2cos²A = 1 + tan²B

⇒ 2cos²A = sec²B [ ∵ sec²Ф = 1 + tan²Ф ]

⇒2cos²A.cos²B =1 [ ∵ secФ = 1/cosФ ]

⇒2cos²B = sec²A

= cos²B + cos²B = 1 + tan²A

⇒ cos²B + cos²B - 1 = tan²A

⇒cos²B - (1 - cos²B) = tan²A

⇒ cos²B - sin²B = tan²A

Hence proved//

Option c. The quantity of gasoline supplied at each price will change.

Step-by-step explanation:

There is a close correlation between the demand and supply. In simple terms, the demand increases inversely to the supply. This causes the price of the goods and commodities to shift. The precise term is inflation - the increase in the price of goods due to the decrease in the supply and increase in demand.