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Let f(θ) = 12 sin θ - 5 cos θ
We know that
Hence, minimum and maximum values of 12 sin θ - 5 cos θ are -13 respectively.
Let f(θ) = 12 cos θ + 5 sin θ + 4
⟹ -13 ≤ 12 cos θ + 5sin θ ≤ 13
⟹ -13 + 4 ≤ 12 cos θ + 5sinθ + 4 ≤ 13 + 4
⟹ -9 ≤ 12 cos θ + 5sinθ + 4 ≤ 17
⟹ -9 ≤ f(θ) ≤ 17
Hence, minimum and maximum values of 12 cos θ + 5 sin θ + 4 are – 9 and 17 respectively.
⟹ -3 ≤f (θ) ≤ 11
Let f(θ) = sin θ - cos θ + 1. Then,
f(θ) = sin θ + (-1) cos θ + 1
= (-1) cos θ + sin θ + 1
Hence, minimum and maximum values of sin θ - cos θ + 1 are 1 - √2 and 1 + √2 respectively.
Let f(θ) = √3 sin θ - cos θ
Again,
Let f(θ) = cos θ - sin θ
Let f(θ) = 24 cos θ + 7 sin θ
We have
sin100° - sin10°
Dividing and multiplying the above equation with above value
We know that maximum and minimum value of any cosine term is +1 and -1
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Chapter 7: Trigonometric Ratios of Compound Angles...