Question #11b8e
2 Answers
See the answer below...
Explanation:
tan^-1([sqrt{1+x^2}-sqrt{1-x^2}]/ [sqrt{1+x^2}+sqrt{1-x^2}])=x
=>([sqrt{1+x^2}-sqrt{1-x^2}]/ [sqrt{1+x^2}+sqrt{1-x^2}])=tanx
=>[sqrt{1+x^2}+sqrt{1-x^2}]/ [sqrt{1+x^2}-sqrt{1-x^2}]=1/tanx
=>sqrt(1+x^2)/sqrt(1-x^2)=(1+tanx)/(1-tanx) [ADDITION-DIVISION METHOD]
=>(1+x^2)/(1-x^2)=(1+tanx)^2/(1-tanx)^2
=>1/x^2=((1+tanx)^2+(1-tanx)^2)/((1+tanx)^2-(1-tanx)^2
=>1/x^2=(2(tan^2x+1))/(4tanx
=>x^2=(2tanx)/(tan^2x+1)
=>x^2=2tanxcdot1/sec^2x
=>x^2=2 cdot sinx/cosxcdotcos^2x
=>x^2=2 cdot sinx cdot cosx
=>x=sqrtsin2x Now what I have to solve...
Explanation:
Hence