Question

sin(40°25')cos(19°35')+cos(40°25')sin(19°35')​

Answer 1

Answer:

√3/2

Step-by-step explanation:

sin(A+B)=sinAcosB+cosAsinB

here A=40°25' and B= 19°35.

substitute in above equation we get

sin(40°25')cos(19°35')+cos(40°25')sin(19°35)=sin(40°25'+19°35')

                                                                        =sin(59°60')

but 60'=1°

so sin(59°60')= sin(60)=√3/2

Answer 2

Answer: √3 / 2

Concept : Trigonometric Identities

Given : sin(40°25')cos(19°35') + cos(40°25')sin(19°35')

To Find : Value of the given identity

Step-by-step explanation:

We know that, according to the identity :

⇒ sinAcosB + cosAsinB = sin(A + B)   ...(i)

Let A=40°25' and B= 19°35.

Putting values in equation (i) :

= sin(40°25')cos(19°35')+cos(40°25')sin(19°35)

= sin(40°25'+19°35')

= sin(59°60')

We know that,  60'=1°

⇒ sin(59°60')= sin(60°)

∴ Value of sin(60°) = $\frac{\sqrt{3} }{2}$

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