Menu Close

If-cot-x-tan-x-4-then-cot-2-2-sin-2x-tan-2-x-




Question Number 193533 by horsebrand11 last updated on 16/Jun/23
   If cot x−tan x=4 then      cot^2 +(2/(sin 2x)) −tan^2 x =?
Ifcotxtanx=4thencot2+2sin2xtan2x=?
Answered by MM42 last updated on 16/Jun/23
1−tan^2 x=4tanx⇒tan^2 x+4tanx−1=0  tanx=−2±(√5)  A=(1/(tan^2 x))+((1+tan^2 x)/(tanx)) −tan^2 x
1tan2x=4tanxtan2x+4tanx1=0tanx=2±5A=1tan2x+1+tan2xtanxtan2x
Answered by Rajpurohith last updated on 19/Jun/23
say a=tanx and b=cotx ⇒ab=1  given b−a=4   ⇒(b+a)^2 −(b−a)^2 =4ab=4  ⇒(b+a)^2 −16=4 ⇒b+a=2(√5)  ⇒2b=4+2(√(5 )) ⇒ b=cotx=2+(√5)  ⇒a=tanx=−2+(√5)  ⇒cot^2 x−tan^2 x=(b+a)(b−a)=2(√5).4=8(√5)  so sin2x=((2a)/(1+a^2 ))=((2(√5)−4)/(1+4+5−4(√5)))=((2((√5)−2))/(10−4(√5)))  =((2((√5)−2))/( 2(√5)((√5)−2)))=(1/( (√5)))  ⇒the value of given expression is  (2+(√5))^2 +2(√5)−(−2+(√5))^2   =2(√5)+(2(√5))(4)=10(√5)      ■
saya=tanxandb=cotxab=1givenba=4(b+a)2(ba)2=4ab=4(b+a)216=4b+a=252b=4+25b=cotx=2+5a=tanx=2+5cot2xtan2x=(b+a)(ba)=25.4=85sosin2x=2a1+a2=2541+4+545=2(52)1045=2(52)25(52)=15thevalueofgivenexpressionis(2+5)2+25(2+5)2=25+(25)(4)=105◼

Leave a Reply

Your email address will not be published. Required fields are marked *