If 7sin θ + 24cos θ = 25 ; then find value of tan θ

 \(\frac{7}{24}\)

7sin θ + 24cos θ = 25

⇒ \(\frac{7}{25}\)sin θ + \(\frac{24}{25}\)cos θ = 1 .....(i)

*(sin²θ + cos²θ = 1)*

Therefore, from (i)

sin θ = \(\frac{7}{25}\) &

cos θ = \(\frac{24}{25}\)

⇒  tan θ = \(\frac{sin θ}{cos θ}\) = \(\frac{\frac{7}{25}}{\frac{24}{25}}\) = \(\frac{7}{24}\)