Question

If tanh x = sin theta, show that sinh x = tan theta, cosh x = sec theta.
with good explanation ​

Answer 1

Step-by-step explanation:

⇒1−tanh2(x/2)1+tanh2(x/2)=secθ ⇒tanh2(x /2)=secθ+1secθ−1=1+cosθ1−cosθ ⇒tanh 2(x/2)=2cos2θ/22sin2θ/2=tan2(θ/2).

Answer 2

Given: Given expression is tan(hx)=sinA and sin(hx) =tanA

To find: We have to show that cos(hx) =secA.

Solution:

We know that tanA is a ratio of sinA to cosA.

so, we can write-

$tan(hx) = \frac{sin(hx)}{cos(hx)}$

Given that

$tan(hx) = sinA \\ \frac{sin(hx)}{cos(hx)} = sinA \\ sin(hx) = sinA.cos(hx)$

Again given expression is sin(hx) =tanA.

Putting the value of sin(hx) we get-

$sin(hx) = sinA.cos(hx) \\ tanA =sinA.cos(hx) \\ \frac{sinA}{cosA} = sinA.cos(hx) \\ cos(hx) = secA$

So, cos(hx) =secA is proved.