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!