Question

if cos theta + sin theta is equal to root 2 * cos theta show that tan theta is equal to root 2 minus 1​

Answer 1

Question

If cos∅ + sin∅ = √2cos∅,show that tan∅ = √2 - 1

Solution

Given Equation,

cos∅ + sin∅ = √2 cos∅

Dividing both sides by cos∅,we write :

→ 1 + tan∅ = √2

→ tan∅ = √2 - 1

Henceforth,Proved

Answer 2

Answer:

${\boxed{\bold{Answer\::}}}$

Given that,

• $\bold\red{Cos\theta + Sin\theta=\sqrt{2}\times Cos\theta}$

To show,

• $\bold\green{tan\theta=\sqrt{2}-1}$

Solution:-

$\tt Cos \theta + Sin \theta = \sqrt{2} \times Cos \theta \\ \\ *By \:dividing\:each\:side\:by \:Cos \theta \\ \\ \rightarrow\tt 1 + \frac{Sin\theta}{Cos \theta} = \sqrt{2} \\ \\ \rightarrow\tt 1 + tan \theta = \sqrt{2} \: \: \: \: [\because tan \theta=\frac{Sin \theta}{Cos\theta}] \\ \\ \rightarrow\tt tan \theta = \sqrt{2} - 1 \: \: \: \:[Showed]$

$\therefore\bold{\underline{tan\theta=\sqrt{2}-1 \: \: \:[Showed]}}$