If (tanθ + secθ) = 7, θ is acute angle than find the value of 5sinθ.

\(\frac{24}{5}\)

 sec²θ - tan²θ = 1

(secθ + tanθ)(secθ - tanθ) = 1

(7)(secθ - tanθ) = 1

(secθ - tanθ) = \(\frac{1}{7}\)

secθ + tanθ = 7  ...(i)

secθ - tanθ = \(\frac{1}{7}\)  ...(ii)

Adding eq. (i) and (ii)

2secθ = \(\frac{50}{7}\)

secθ = \(\frac{25}{7}\)=\(\frac{H}{B}\)

P = 24

5sinθ = 5×\(\frac{24}{25}\)

= \(\frac{24}{5}\)