If secθ + tanθ = a, then tanθ is -

Question: If secθ + tanθ = a, then tanθ is -

Solution:
দেওয়া আছে,
secθ + tanθ = a ................. (1)

আমরা জানি,
sec²θ - tan²θ = 1
বা, (secθ + tanθ)(secθ - tanθ) = 1
বা, a(secθ - tanθ) = 1
বা, secθ - tanθ = 1/a ................ (2)

(1) - (2) হতে পাই,
(secθ + tanθ) - (secθ - tanθ) = a - (1/a)
বা, 2tanθ = (a² - 1)/a
বা, 2tanθ = (a² - 1)/a
∴ tanθ = (a² - 1)/2a