Question

Evaluate: sin 25° cos 65° + cos 25° sin 65°.​

Answer 1

$\huge⚘ \bf \ \red{Answer}$

sin25⁰ cos65⁰ +cos25⁰ sin65⁰

= sin25⁰ sin(90⁰−65⁰)+cos25⁰ cos(90⁰−65⁰)

= sin25⁰ sin25⁰ +cos25⁰ cos25⁰

=sin²25⁰ + cos²25⁰

= 1

Answer 2

sin 25° cos 65° + cos 25° sin 65°

= sin 25° cos (90° – 25°) + cos 25° sin (90° – 65°)

= sin 25° sin 25° + cos 25° cos 25°

= sin2 25° + cos2 25°

= 1 [By trigonometry identity: sin2 x + cos2 x = 1]