Q. 193.9( 10 Votes )

# If sec x cos 5x +

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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