Answer :

Given,


sec x cos 5x = -1


cos 5x = -1/sec x


cos 5x + cos x = 0 { sec x = 1/cos x}


By transformation formula of T-ratios we know that –


cos A + cos B =



2 cos 3x cos 2x = 0


cos 3x = 0 or cos 2x = 0


0 < x ≤ π/2


0< 2x ≤ π or 0< 3x ≤ 3π/2


2x = π/2


x = π/4


3x = π/2


x = π/6


Or 3x = 3π/2


x = π/2


Hence, x = π/6, π/4.


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