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This is a question from the chapter trigonometry. Can any one solve it.
In this question the need is to simplify both the equations first individually and then after certain amount of simplfication equating both of them.STEP 1Divide the first equation throughout by cos2.Then, the equation will be:a tan2 + b = m(1 + tan2)By, simplyfication:(a – m) tan2 = m – b.......(3)STEP 2Divide the first equation throughout by cos2.Then, the equation will be:b tan2 + a = n(1 + tan2)By, simplyfication:(b – n) tan2 = n-a ........(4)STEP 3Simplification of condition given:a tan = b tantan2/tan2 = b2/a2…......(5)STEP 4Divide equations (3) and (4), then inject the equation (5) in the new equation:(a – m)(b2)(n – a) = (m – b)(a2)(b – n) ab2n – mnb2 – a2b2 + amb2 = amb2 – a2mn – a2b2 + a2bn ab2n + a2mn – mnb2 – nba2 = 0 a2n(m – b) + b2n(a – m) = 0 a2n (m – b)= b2n(m – a) THE FINAL EQUATION IS: a2/b2=(m-b)/(m-a)
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