Question

prove that
(1+tan15°)(1+tan30°)=2

​

Answer 1

Answer:

2

Step-by-step explanation:

tan (A+B) = (tanA + tanB)/(1-tanA×tanB )

here A= 30, B= 15

tan(45) = (tan30 + tan 15)/(1-tan30×tan15)

and we know that tan(45) =1

So, 1 = ( tan30 + tan 15)/(1-tan30×tan15)

Taking denominator to the Right hand side

(1-tan30×tan15) = ( tan30 + tan 15)

Hence, tan30 + tan 15+ tan30×tan15=1

(1+0.58)(1+ 0.27)

=>1.58 x 1.27

=>2 (Proved)

I hope it will help you

Answer 2

To prove:-

• $\bf (1+tan15°)(1+tan30°)=2$

Proof:-

We know that

$\boxed{\bf 15°+30°=45°}$

$\sf{:}\implies tan (15°+30°)=tan45°$

$\sf{:}\implies \dfrac {tan15°+tan30°}{1-tan15°.tan30°}=1$

$\sf{:}\implies tan15°+tan30°=1-tan15°.tan30°$

$\sf{:}\implies tan15°+tan30°+tan15°.tan30°=1$

$\sf{:}\implies 1+tan15°+tan30°+tan15°.tan30°=1+1$

$\sf{:}\implies 1+tan15°+tan30°+tan15°.tan30°=2$

$\sf{:}\implies 1 (1+tan15°)+tan30°(1+tan15°)=2$

$\sf{:}\implies (1+tan15°)(1+tan30°)=2$

$\therefore{\huge{ \bf{(Proved)}}}$