Q) If tan θ =24/7, then find the value of sin θ + cos θ.

(Q 22 A – 30/1/3 – 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 θ =

∴ We can assume that Opposite side = 24 k and adjacent side = 7 k 

here, k is a positive integer

Step 2: Now, by pythagorus theorem,

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

∴ (Hypotenuse) ² = (24 k) ² + (7 k) ² = (576 k ² + 49 k ² ) = ( 625 k ² )

∴  Hypotenuse = √( 625 k ²) = 25 k

Step 3: Value of sin θ =

=

Similarly, Value of cos θ =

=

Step 4: Now, we need to calculate the value of sin θ + cos θ

By substituting the values of sin θ and cos θ from step 3, we get:

sin θ + cos θ =

Therefore, value of (sin θ + cos θ) is .

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