If sec (5α - 15°) = cosec (15° - 2α) then the value of cosα + sin 2α + tan (1.5α).

\(\sqrt {3}\) + 1

[Concept: sec A = cosec B, when A + B = 90°]

Therefore,

(5α - 15° + 15° - 2α) = 90°

3α = 90°

α = 30°

Put this value in find →

⇒ cosα + sin 2α + tan (1.5α)

⇒ cos30° + sin60° + tan45°

= \(\frac{\sqrt {3}}{2}\) + \(\frac{\sqrt {3}}{2}\)  + 1

= \(\sqrt {3}\) + 1