Question

"Question8
Evaluate, sin60° cos 30° + cos60° sin 30°
Chapter 6, Trigonometry, Exercise -6, Page number -288"

Answer 1

Hey there!

We know that,
sin(A + B) = sinA cosB + cosA sinB.

In the given question,
sin60 cos30+ cos60 sin30 is in the form of sinAcosB + cosA sinB = sin ( A + B)

So,

sin60° cos 30° + cos60° sin 30°

= sin ( 60 + 30 )

= sin ( 90 )

We know that, sin90° = 1

Finally, sin90° = 1 .

= 1 .

( or)

cos30 = sin(90- 30 ) = sin60
sin30 = cos( 90- 30 ) = cos60

So, sin60° cos 30° + cos60° sin 30°
= sin²60 + cos²60
= 1. [ sin²A + cos²A = 1 ]


Therefore, sin60° cos 30° + cos60° sin 30° = 1 .

Answer 2

HELLO DEAR,



we know that:-
sinAcosB + cosAsinB = sin(A + B)

now,

sin60°cos30° + cos60°sin30°

=> sin(60° + 30°) = sin90° = 1



ANOTHER METHOD,



sin60° cos 30° + cos60° sin 30°


=> √3/2 × √3/2 + 1/2 × 1/2

=> 3/4 + 1/4

=> (3 + 1)/4

=> 4/4 = 1

I HOPE ITS YOU DEAR,
THANKS