Explanation:

From the given equation,
sec α + tan α = 2
∴ 1/cos α + sin α /cos α = 2
∴ 1 + sin α /cos α = 2
⇒ 1 + sin α = 2 cos α
Squaring both sides, we get
⇒ (1 + sin α)² = (2 cos α)²
⇒   1 + sin² α + 2 sin α = 4 cos² α
⇒ 1 + sin² α + 2 sin α = 4 (1 – sin ² α)
⇒   1 + sin² α + 2 sin α = 4 – 4 sin ² α
⇒ 5 sin² α + 2 sin α – 3 = 0
By the rule of factorization,
(sin α + 1)(5 sin α – 3) = 0
sin α = – 1 or 3/5
Since 0 < α < 90, then sin α > 0
So, sin α = 3/5 = 0.6