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sin24°+cos6°=(√15+√3)/4 . prove that lhs =rhs. pls give the complete steps

sin24°+cos6°=(√15+√3)/4 . prove that lhs =rhs. pls give the complete steps

Grade:11

1 Answers

Bhumiti
34 Points
4 years ago
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.

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