Math, asked by smanu2277, 1 month ago

7sinx+24cosx=25, find sinx+cosx

Answers

Answered by farjeekhata
0

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 anjumanyasmin
1

Given:

7sinx+24cosx=25,

find sinx + cosx

we have  

7sinx+24cosx=25

Divide both sides by 25

\frac{7}{25}\ sinx  +\frac{24}{25}\ cosx = \frac{25}{25}

we get

\frac{7}{25}\ sinx  +\frac{24}{25}\ cosx = 1   -(1)

We know that

sin^{2}\ x +cos^{2}\ x=1

so we can write it as

sinx.sinx+cosx.cosx=1   -(2)

Comparing equation (1) and (2) we get

sinx=\frac{7}{25}\\\\cosx=\frac{24}{25}

Now sinx+cosx

=\frac{7}{25}+ \frac{24}{25}

=\frac{7+24}{25}

=\frac{31}{25}

Hence the value of  sinx+cosx is \frac{31}{25}

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