Question

if sin(a+b)=sina.cosb+cosa.sinb and cos(a b)= cosA.cosB+sinA.sinB find the value of sin 75 and cos 15

Answer 1

Hello users.....

we have to find the value of 

sin 15° and cos 15° = ? 

solution:-

we know that

sin(A-B)=sinAcosB-cosAsinB

and

 cos(A-B)=cosAcosB+sinAsinB

now,

(1) sin 15° = sin ( 45° - 30°)

= sin 45°cos 30° - cos 45° sin 30°

=1/√2 × √3/2 - 1/√2 × 1/2

= √3 / 2√2 - 1 / 2√2

= ( √3 - 1) / 2√2 answer 

(2) cos 15° = cos(45° - 30°)

= cos 45° cos 30° + sin 45° sin 30°

= 1 / 2√2 × √3 / 2  + 1 / √2 × 1 / 2

= √3 / 2√2 + 1 / 2√2 

= ( √3 + 1) / 2√2 answer

✰✰ hope it helps ✰✰ 

#Dramaqueen⭐

Answer 2

heya...

✔here is ua answer:

__________________________________________❤

15° can be written as 45° - 30°, Let A = 45°, and B = 30°

we know that Sin(A-B) = SinACosB - CosASinB,

and Cos A = root 1-SinA^2

Substitute A and B here,

Sin(45-30) = (1/√2)*(√3/2) - (1/√2)*(1/2),

Sin (15) = (√3 - 1)/(2√2),

Similarly Cos 15 = (1+√3)/(2√2)

hope it helps..!!❤