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Find the range of 7 cos x - 24 sin x +5...

Find the range of `7 cos x - 24 sin x +5`

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Find the maximum and the minimum values of the following function over R. (i) sin^(2) X (ii) 7 cos x -24 sin x + 5 (iii) 3 sin x-4 cos x (iv) 3 cos (4x -5) + 4 (v ) (sin x+ cos x) (vi) 5 sin x + 12 cosx + 13 (vii) (3 sin^(2) x+ 4) (ix) 5 sin x + 12 cos x -13

Show that the range of the function f(x ) = (sin^(2) x + cos^(4) x)/( cos^(2) x+ sin^(4) x ) is a singleton set.