If cot A+ tan A = m sec A – cos A = n , prove that:
(m²n)^2/3-(mn²)^2/3 = 1.

Question

If cot A+ tan A = m sec A – cos A = n , prove that: (m 2 n) 2/3 -(mn 2 ) 2/3 = 1.

Arun · Answer

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

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If cot A+ tan A = m sec A – cos A = n , prove that: (m 2 n) 2/3 -(mn 2 ) 2/3 = 1.

If cot A+ tan A = m sec A – cos A = n , prove that:
(m²n)^2/3-(mn²)^2/3 = 1.

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If cot A+ tan A = m sec A – cos A = n , prove that: (m 2 n) 2/3 -(mn 2 ) 2/3 = 1.

If cot A+ tan A = m sec A – cos A = n , prove that:(m2n)2/3-(mn2)2/3 = 1.

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If cot A+ tan A = m sec A – cos A = n , prove that:
(m²n)^2/3-(mn²)^2/3 = 1.