Question Details

Given acute angles A and B such that sinA=35 and cosB=45, find the value of sinAcosB+cosAsinB:

Options

A

12/25

B

1

C

24/25

D

7/25

Show Answer

Correct Answer :

Option C

24/25

120/169

Solution :

The correct answer is 24/25.

We are given that A and B are acute angles with:

sinA=35

and

cosB=45

Since A is an acute angle, its cosine value cosA must be positive. We can find cosA using the Pythagorean trigonometric identity:

cosA=1-sin2A

cosA=1-352=1-925=1625=45

Similarly, since B is an acute angle, its sine value sinB must also be positive:

sinB=1-cos2B

sinB=1-452=1-1625=925=35

Now, we substitute these trigonometric values into the expression sinAcosB+cosAsinB:

sinAcosB+cosAsinB=3545+4535

=1225+1225

=2425

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