Question

prove that sin9+cos9=√2(sin54)

Answer 1

$\sin(9 ) + \cos(9) ) {}^{2} = 2 \sin(54) \\ \\ \\ so. \\ \\ 1 = 2sin54$

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Answer 2

Answer:

54°-9°=45°

or, 54°=45°+9°

or, tan54°=tan(45°+9°)

or, tan54°=tan45°+tan9°/1-tan45°tan9°

or, tan54°=1+tan9°/1-tan9° [∵, tan45°=1]

or, tan54°=(1+sin9°/cos9°)/(1-sin9°/cos9°)

or, tan54°={(cos9°+sin9°)/cos9°}/{(cos9°-sin9°)/cos9°}

or, tan54°=cos9°+sin9°/cos9°-sin9° (Proved)