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:

Since we are given that tan A =

∴ 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 =

=

Therefore, value of sin A is .

Step 4: Value of cos A =

=

Therefore, value of cos A is .

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