y = 7 cos x + 24 sin x
y2 = (7 cos x + 24 sinx)2
= 49 cos2x + 576 sin2x + 2 × 7× 24 cos x sin x
= 49 – 49 sin2 x + 576 – 576 cos2 x + 2 × 7 × 24 cos x sin x
= 625 – (7 sin x – 24 cos x)2
∴ Maximum value = 25
For maximum value
Cos x = \(\frac{-7}{25}\) and sin x =\(\frac{-24}{25}\)
∴ Minimum value = 7(\(\frac{-7}{25}\)) + 24 (\(\frac{-24}{25}\))
\(=\frac{-49-576}{25}\) = -25
∴ Minimum value = – 25