Question

sin 24°+ cos 6°=
1. √15+√3/4 3.√15-3/4
2.√15+3/4 4. √15-√3/4​

Answer 1

Answer:

Lhs=sin24°+cos6° =sin(90-66)°+cos6°. [We can write sin(90-66)°as cos(66)°.] We get lhs= cos66°+cos6° now just apply formula of cosC+cosD=2cos[(C+D)\2].cos[(C-D)\2] above.. We get cos66°+cos6°=2cos[(66+6)\2]×cos[(66-6)\2] = 2cos36°×cos30°= 2×(√5+1)\4×√3\2 = (√5+1)√3\4. Ask freely if any doubt.