If cot A+ tan A = m sec A – cos A = n , prove that:(m2n)2/3-(mn2)2/3 = 1.
Malyarpita Singh , 6 Years ago
Grade 10
10 grade maths> If cot A+ tan A = m sec A – cos A = n , p...
1 AnswersArun
Last Activity: 6 Years ago
Given cot theta +tan theta = m
1/tan theta+ tan theta = m.........(1)
sec theta - cos theta = n
sec theta - 1/ sec theta = n ........(2)
Using equation (1) and (2)
(m^2n)^(2/3)-(mn^2)^(2/3)
((1/tan theta+ tan theta)^2(sec theta - 1/ sec theta))^(2/3)-((1/tan theta+ tan theta)(sec theta - 1/ sec theta)^2)^(2/3)
(1/cos^6 theta)^(1/3)-(sin^6 theta/cos^6 theta)^(1/3)
sec^2 theta-tan^2 theta
=1
1/tan theta+ tan theta = m.........(1)
sec theta - cos theta = n
sec theta - 1/ sec theta = n ........(2)
Using equation (1) and (2)
(m^2n)^(2/3)-(mn^2)^(2/3)
((1/tan theta+ tan theta)^2(sec theta - 1/ sec theta))^(2/3)-((1/tan theta+ tan theta)(sec theta - 1/ sec theta)^2)^(2/3)
(1/cos^6 theta)^(1/3)-(sin^6 theta/cos^6 theta)^(1/3)
sec^2 theta-tan^2 theta
=1
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