Question

find the solution of following equation tanx+secx=2cosx

Answer 1

Answer : x = π / 6 or 5π / 6

Solution :

tanx = sin x / cos x

sec x = 1 / cos x

Therefore

sin x / cos x + 1 / cos x = 2 cos x

( sin x + 1 ) / cos x = 2 cos x

sin x + 1 = 2 cos^2 x

sin x + 1 = 2 ( 1 - sin^2 x)

sin x + 1 = 2 - 2sin^2 x

Let sin x = Y

y + 1 = 2 - 2y^2

2y^2 + y - 1 = 0

y^2 + y/2 -1/2 = 0

y^2 + y - y/2 - 1/2 = 0

y ( y + 1) -1/2 ( y + 1 ) = 0

( y + 1 ) ( y - 1/2 ) = 0

y = -1 or y = 1/2

sin x = - 1 or sin x = 1/2

x = 3π / 2 or x = π / 6 = 5π / 6

But x can't be ( 2n + 1) π / 2

Therefore x = π / 6 or 5π / 6

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