Question

Prove that ---> sin 25°+cos 5° = √3 sin55° ​

Answer 1

L.H.S = cos5 – sin 25

= sin 95 – sin 25 [ sin(90+5) = cos5 ]

= 2 * cos (95+25)/2 * sin (95-25)/2

= 2 * cos60 * sin35

=2 * ½ * sin35 (cos60 = ½ )

= sin35

= R.H.S

hence L.H.S = R.H.S

Answer 2

Step-by-step explanation:

sin 25°+cos 5° =sin 25°+sin85° = sin85+sin 25°

☆ cos 5° = cos( 90°- 85°)

☆ cos (1×90°-85°)

☆ odd multipul of 90 so cos

change into sin

☆ angle lies in 1st quadrant so

positive sign

sin85°+sin 25°

☆ sinP + sinQ = 2sin (P+Q)/2 cos (P-Q)/2

sin85°+sin 25°= 2sin (85°+25°)/2 cos( 85°-25° )/2

= 2sin 110°/2 cos 60°/2

= 2sin 55° cos 30°

= 2sin 55° √3 /2 ☆ cos 30° = √3 /2

= sin 55° √3

√3 sin 55° = √3 sin 55°

L.H.S = R.H.S