Question

What is the simplified value of 1 + tan a tan (a/2)?

Answer 1

1+tan a/2 is the answer...

hope it helps

Answer 2

Answer:

$1+(\text{tan} a )(\text{tan}\frac{a}{2})=seca$

Step-by-step explanation:

Given : Expression - $1+(\text{tan} a )(\text{tan}\frac{a}{2})$

To simplify : The given expression

Step 1- Write the expression

$1+(\text{tan} a )(\text{tan}\frac{a}{2})$

Step 2 - Solve the expression by applying property of trigonometry

$=1+(\frac{sina}{cosa})(\frac{sin\frac{a}{2}}{cos\frac{a}{2}})$

$=\frac{(cosa)(cos\frac{a}{2})+(sina)(sin\frac{a}{2})}{(cosa)(cos\frac{a}{2})}$

Step 3 - Applying $(cosx)(cosy)+(sinx)(siny)= cos(x-y)$

$=\frac{cos(a-\frac{a}{2})}{(cosa)(cos\frac{a}{2})}$

$=\frac{cos(\frac{a}{2})}{(cosa)(cos\frac{a}{2})}$

Step 4- $cos\frac{a}{2}$ cancel out

$=\frac{1}{cosa}$

$=seca$

Therefore,  $1+(\text{tan} a )(\text{tan}\frac{a}{2})=seca$