7sinx+24cosx=25, find sinx+cosx
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Step-by-step explanation:
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 = − 7 25 −725 and sin x = − 24 25 −2425 ∴ Minimum value = 7( − 7 25 −725) + 24 ( − 24 25 −2425) = − 49 − 576 25 =−49−57625 = -25 ∴ Minimum value = – 25
Answered by
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Given:
7sinx+24cosx=25,
find sinx + cosx
we have
7sinx+24cosx=25
Divide both sides by 25
we get
-(1)
We know that
so we can write it as
-(2)
Comparing equation (1) and (2) we get
Now
Hence the value of is
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