Question

Prove (tanA+2)(2tanA+1)=5tanA+2sec^2 A

Answer 1

Answer:

$\bf(tanA+2)(2tanA+1)=2\,sec^2A+5\,tanA}$

Step-by-step explanation:

$\text{consider,}$

$(tanA+2)(2tanA+1)$

$\text{By term by term multiplication we get}$

$=2\,tan^2A+tanA+4\,tanA+2$

$=2\,tan^2A+2+5\,tanA$

$=2(tan^2A+1)+5\,tanA$

$\text{Using,}$

$\boxed{\bf\,sec^2\theta-tan^2\theta=1\implies\,sec^2\theta=1+tan^2\theta}$

$\text{we get}$

$=2\,sec^2A+5\,tanA$

$\implies\boxed{\bf(tanA+2)(2tanA+1)=2\,sec^2A+5\,tanA}$