Question

if tan theta= 4/3 , show that (sin theta +cos theta) =7/5

Answer 1

¥hey there!!

Given that: tanx =4/3 ------(1)

so we know that .

===) tanx = p/b -------(2)

comparing both equation..we get.

p=4 , b= 3

now using Pythagoras theorem

h² = b² + p²

h = √(3²+4²) = 5

now using trigonometric ratios rule

sinx = p/h = 4/5 ------(a)

cosx =b/h = 3/5 ----(b)

hence , adding both equation (a) +(b)

=> sinx+cosx = 4/5 + 3/5 = 7/5

proved..

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⭐Hope it will help you

Answer 2

Theta is written as A in the given solution ,





Given, tan A = 4 / 3


$\frac{height}{base} = \frac{4}{3}  \:\:\:\:\:\:\:\:\:\:\:\:\:\:\: |  \:\:\: tan\: A = \frac{height}{base}$




Now,

Let height is 4x and base 3x ,


By Pythagoras Theorem,

( 4 x )^2 + ( 3 x )^2 = Hypotenuse^2

25 x^2 = hypotenuse^2

5 x = Hypotenuse

Hence,$sin \; A = \frac{height}{hypotenuse} \;\;\;\;\;\;\;\;\;\;\;\; | \;\; sin \;A = \frac{height}{hypotenuse}$

sin A = $\frac{4x}{5x} = \frac{4}{5}$

cos A = $\frac{base}{hypotenuse}$

cos A = $\frac{3x}{5x} = \frac{3}{5}$

So,

sin A + cos A

→ $\frac{4}{5}  + \frac{3}{5}$

→ $\frac{ 4 + 3}{5}$

→ $\frac{7}{5}$

Hence proved that sin theta + cos theta is equal to $\frac{7}{5}$