If sec (6α - 25°) = cosec (25° - 3α) then the value of cosα .

1 \(\frac{\sqrt {3}}{4}\)  \(\frac{\sqrt {5}}{2}\)  \(\frac{\sqrt {3}}{2}\)

\(\frac{\sqrt {3}}{2}\)

[Concept: sec A = cosec B, when A + B = 90°] Therefore, (6α - 25° + 25° - 3α) = 90° 3α = 90° α = 30° Put this value in find → ⇒ cosα  ⇒ cos30°  = \(\frac{\sqrt {3}}{2}\)