Question

Q. 4) Refer following question with
option and mark appropriate option.
4) Which of the following is correct
A) sin(45)º cos(45)° = sin(90)°
B) sin(30) cos(30)° = sin(60)°
C) sin(45)° + cos(45)° = sin(90)°
D) 2 sin(30)° cos(30)° = sin(60)
O A is correct
o
B is correct
C is correct
D is correct​

Answer 1

Answer:

D IS CORRECT

Step-by-step explanation:

(A) sin 45 cos 45 = sin 90

sin 45 = 1/√2

cos 45 = 1/√2

hence sin 4 5 cos 45 = 1/2

and sin 90 = 1.

HENCE A IS FALSE.

(B) sin 30 cos 30 = sin 60

sin 30 = 1/2

cos 30 = √3/2

hence sin 30 cos 30 = √3/4

and sin 60 = √3/2

HENCE B IS ALSO FALSE

(C) sin 45 + cos 45 = sin 90

sin 45 = 1/√2

cos 45 = 1/√2

sin 45 + cos 45 = 2/√2 = √2 and sin 90 = 1

so C IS ALSO FALSE.

(D) 2sin30cos30 = sin 60

2 sin 30 cos 30 = 2 × 1/2 × √3/2 = √3/2

and sin 60 = √3/2

HENCE D IS CORRWCT