If 7 θ+24 θ=25, then what is the value of ( θ+ θ) ? [NDA-I 2021]

Correct Answer is : 312531/252531

Correct Answer is : 312531/252531

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UPSC NDA I 2021 Mathematics Solved Paper

Question : 42 of 120

Marks: +1, -0

7 \sin \theta+24 \cos \theta=25

(\sin \theta+\cos \theta)

Solution: 👈: Video Solution

Concept:

\sin \theta = \frac{\text{ Perpendicular }}{\text{ Hypotenuse }}

\cos \theta = \frac{\text{ Base }}{\text{ Hypotenuse }}

\sin^2 \theta+\cos^2 \theta=1

Calculation:

7 \sin \theta+24 \cos \theta=25

Dividing by 25 on boththe sides, we get

\frac{7}{25} \sin \theta+\frac{24}{25} \cos \theta=1

. . . (i)

We know that,

\sin^2 \theta+\cos^2 \theta=1

\sin \theta \cdot \sin \theta+\cos \theta \cdot \cos \theta=1

. . . (ii)

On comparing equ (i) and (ii)

\sin \theta = \frac{7}{25}

\cos \theta = \frac{24}{25}

Now,

(\sin \theta+\cos \theta)

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

= \frac{31}{25}

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