**If tan = 4/3, find the value of sin **θ** + cos **θ** (both sin **θ** and cos **θ** are positive).**

**Answer :**

Let ∆ABC be a right angled

∠ACB = θ

Given that, tan θ = 4/3

(AB/BC = 4/3)

tan θ = 4/3

(AB/BC = 4/3)

Let AB = 4x,

then BC = 3x

In right angled ∆ABC

AC^{2} = AB^{2 }+ BC^{2}

⇒ AC^{2 }= AB^{2 }+ BC^{2}

⇒ AC^{2} = AB^{2} + BC^{2}

⇒ AC^{2 }= AB^{2 }+ BC^{2}

⇒ (AC^{2 }= (4x)^{2} + (3x)^{2}

⇒ AC^{2 }= 16x^{2 }+ 9x^{2}

⇒ AC^{2} = 25x^{2}

⇒ AC^{2} = (5x)^{2}

⇒ AC = 5x

Sin θ = perpendicular/Hypotenuse

= AB/AC

= 4x/5x

= 4/5

cos θ = Base/Hypotenuse

= BC/AC

= 3x/5x

= 3/5

sin θ + cos θ

= 4/5 + 3/5

= (4 + 3)/5

= 7/5

Hence,

Sin θ + cos θ = 7/5 = 1 2/5

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