This is the basic and conceptual question from trigonometric ratios in which we have given that if tanθ=4/3, we have been asked to show that (sinθ+cosθ)=7/5.

RS Aggarwal, Class 10, Chapter 10, question no 18.

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Given,

tanθ=4/3.

cotθ=1/(4/3)=3/4

[ Since, 1/tanθ=cotθ ]

We know that,

tanθ= opposite side to theta / adjacent side to theta.

So, opposite side =4 , Adjacent side =3

Hypotenuse = (4²+3²)=5

Now,

sinθ= Opposite side to theta / Hypotenuse =4/5

cosθ= Adjacent side to theta / Hypotenuse =3/5

To prove : sinθ+cosθ=7/5.

L. H.S

=sinθ+cosθ

=4/5+3/5

=7/5

= R. H. S

Hence proved!