Question

sin (40⁰25¹) cos (10⁰35¹)+ cos (40⁰25¹) sin (19⁰35¹)= options A) 1 B) 3✓2 C) 0 D) –1 please answer me​

Answer 1

Step-by-step explanation:

Given:-

sin (40⁰25¹) cos (19⁰35¹)+ cos (40⁰25¹) sin (19⁰35¹)

To find:-

The value of sin (40⁰25¹) cos (19⁰35¹)+ cos (40⁰25¹) sin (19⁰35¹)

Using formula:-

Sin(A+B)=Sin A Cos B+ Cos A Sin B

Solution:-

Given that:-

sin (40⁰25¹) cos (19⁰35¹)+ cos (40⁰25¹)

sin (19⁰35¹)

This is in the form of SinACosB

+CosASinB

Here, A=40°25' and B=10°35'

We know that

SinACosB +CosASinB=Sin(A+B)

=>sin (40⁰25¹) cos (19⁰35¹)+ cos (40⁰25¹)

sin (19⁰35¹)

=>Sin(40°25'+19°35')

=>Sin(40+19+(25'+35'))

=>Sin(59°+60')

=>Sin(59°+1°)

(since1°=60')

=>Sin60°

=>√3/2

Answer:-

The value is √3/2