Question

"Question7
If tanθ=4/3,Then show that [sinθ+cosθ]=7/5.
Chapter 5 , Trigonometry, Exercise -5 , Page number - 273"

Answer 1

Hey there! Thanks for the question!

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 !

Answer 2

Given,

Tan∅ = 4/3 ------1equation

=================

Tan∅ = height/base

Putting the value of tan∅ from 1equation,

4/3 = height/base

Now,
Let,
height =4x & base = 3x
-------------------------
By Pythagoras theorem,

(4x)²+(3x)²=hypotenuse²
√(25x²) = hypotenuse
5x = hypotenuse

------------------

Main content :-

Sin∅ = height/hypotenuse
Sin∅ = (4x)/(5x) =4/5

Cos∅ = base/hypotenuse
Cos∅= (3x)/(5x) =3/5

Sin∅ + Cos∅

=> 4/5 + 3/5

=> (4+3)/5

=> 7/5

Hence, proved that sin∅ + cos∅=7/5


I hope this will help you


-by ABHAY