If cosA = 5/13 and sinB = 12/13 find sinA cosB + cosA sinB:

Correct Answer is : 120169120/169169120

If cosA = 5/13 and sinB = 12/13 find sinA cosB + cosA sinB:

Correct Answer is : 120169120/169169120

Test Index

SSC CHSL 14 Nov 2025 Shift 2 Paper

Question : 52 of 100

Marks: +1, -0

If cosA =

\frac{5}{13}

and sinB =

\frac{12}{13}

find sinA cosB + cosA sinB:

$\frac{120}{169}$
$\frac{13}{169}$
$\frac{12}{169}$
$\frac{7}{13}$

Validate

Solution:

Concept:

The expression sinA cosB + cosA sinB is the expanded form of sin(A+B) from the sine addition formula. Use the Pythagorean identity sin²θ + cos²θ = 1 to find the missing trigonometric ratios, assuming angles are acute so values are positive.

Explanation:

Given cosA = 5/13. Compute sinA = √(1 − cos²A) = √(1 − 25/169) = √(144/169) = 12/13.

Given sinB = 12/13. Compute cosB = √(1 − sin²B) = √(1 − 144/169) = √(25/169) = 5/13.

Now evaluate: sinA cosB + cosA sinB = (12/13 × 5/13) + (5/13 × 12/13) = 60/169 + 60/169 = 120/169.

Answer:

Option A:

\frac{120}{169}

Go to Question:

Prev Question

Next Question