Question

Prove (2cos12°cos6°)/(1+2sin12°cos6°)=tan54°

Answer 1

Answer:

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$

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)

Answer 2

Answer:

Step-by-step explanation:

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°