If tan A = 4/3, find sin A and cos A

Q) If tan A = 4 / 3, find sin A and cos A.

(Q 25 A – 30/2/3 – CBSE 2026 Question Paper)

Ans:

Step 1: We know that in a right angled triangle, tan θ is given by:

$\tan \theta = \frac{Opposite~side}{Adjacent~side}$

Since we are given that tan A = $\frac{4}{3}$

∴ We can assume that Opposite side = 4 k and adjacent side = 3k

here, k is a positive integer

Step 2: Now, by pythagorus theorem,

(Hypotenuse) ² = (Opposite side) ² + (Adjacent side) ²

∴ (Hypotenuse) ² = (4 k) ² + (3 k) ² = (16 k ² + 9 k ²) = ( 25 k ² )

∴ Hypotenuse = √( 25 k ²) = 5 k

Step 3: Value of sin A = $\frac{Opposite~side}{Hypotenuse}$

= $\frac{4 k}{5 k} = \frac{4}{5}$

Therefore, value of sin A is $\frac{4}{5}$ .

Step 4: Value of cos A = $\frac{Adjacent~side}{Hypotenuse}$

= $\frac{3 k}{5 k} = \frac{3}{5}$

Therefore, value of cos A is $\frac{3}{5}$ .

Hence Proved !

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