Question

prove that sin 15° + cos 15° = whole root 3/2​

Answer 1

Sin(45-30) + Cos(45-30)
Sin45 Cos30 + Cos45 Sin 30
1/sqrt2 . sqrt 3/2 + 1/sqrt2 .1/2
sqrt3/2sqrt2 +1/2sqrt2
(1+sqrt3)/2sqrt2
Rationalising this you get
sqrt2(1+sqrt3)/4

Answer 2

answer √3/√2

explanation

( given) sin 15 + cos 15

divide and multiply with √2

√2(1/√2 x sin 15 + 1/√2 x cos 15 )

√2(cos45 . sin15 + cos15 . sin 45 )

√2(sin15 . cos45 + cos15 . sin 45)

sin(a+b) = ( sina . cosb + casa . sin b)

√ 2 x sin (15+45 )

√2 x √3/2=√2 x√3/√2.√2

= √3/√2