If sin ⁡ hx= tan ⁡A, then | tan ⁡ hx |=

Question

Accepted Answer

Correct answer: A. (a) sinh ⁡x= tan ⁡A tan ⁡A= e^x-e^-x2 ⇒e^x-e^-x=2 tan ⁡A ⇒ (e^x )^2-2 tan ⁡Ae^x-1=0 ⇒e^x= 2 tan ⁡A 4 tan^2 ⁡ A+42 ⇒e^x= 2 tan ⁡A 2 sec ⁡A2 Take, e^x= tan ⁡A+ sec ⁡A ⇒e^-x= 1 tan ⁡A+ sec ⁡A Add both side e^x. e^-x+e^x= 1 sec ⁡A+ tan ⁡A sec ⁡A- tan ⁡A+ tan ⁡A+ sec ⁡A sec ⁡A- tan ⁡A = sec ⁡A- tan ⁡A+ tan ⁡A+ sec ⁡A=2 sec ⁡A Now, tan ⁡ hx= e^x-e^-xe^x+e^x= 2 tan ⁡A2 sec ⁡A= sin ⁡A= | sin ⁡A |

$If sin hx = tan A, then | tan hx | =$

Solution

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