Question

Evaluate:

$\sin25° \cos65° + \cos25° \sin65°$

Answer 1

Heya,

We know that,

sin( A + B ) = sinAcosB + cosAsinB

Given, sin25°cos65° + cos25°sin65°

Let A=25° and B=65°

=sin( 25 + 65 )

= sin90

= 1 Answer...

HOPE IT HELPS:-))

Answer 2

Method - 1:

Given : sin 25° cos 65° + cos 25° sin 65°

⇒ sin 25 cos (90 - 25) + cos 25 sin (90 - 25)

⇒ sin 25 sin 25 + cos 25 cos 25

⇒ sin^2 25 + cos ^2 25

We know that sin^2 A + cos^2 A = 1

⇒ 1.

Method - 2 :

Given : sin ° 25 cos 65° + cos 25° sin 65°

We know that  sinA cos B + cos A sin B = sin(A + B)

⇒ sin(25 + 65)

⇒ sin 90

⇒ 1.

Hope this helps!