Question

in this question x represent theta so pls help me

prove that
cotx.cot(60°-x).cot(60°+x)=cot3x

chapter trigonometry class 11 ​

Answer 1

Step-by-step explanation:

1/tanx × 1/tan(60-x) × 1/tan(60+x)=1/tan3x

• tanx × tan(60-x) × tan(60+x)=tan3x
• tanx × tan60-tanx/1+tan60tanx × tan60+tanx/1-tan60tanx=tan3x
• (because tan(x+y)=tanx+tany/1-tanxtany)
• tanx × (root3-tanx/1+root3tanx) × (root3+tanx/1-root3tanx)=tan3x
• tanx × (root3)²-tan²x/1²-(root3tanx)²=tan3x
• tan(3-tan²x/1-3tan²x)
• 3tanx-tan³x/1-3tan²x
• (this is the formula of tan3x...
• tan3x
• (so...cotx.cot(60-x).cot(60+x)=cot3x)