Question

If sin theta+cos theta is equal to root2 cotheta theta is not equal to 90 then the value theta is

Answer 1

Answer:

22.5

Step-by-step explanation:

I think the question is something clumsy. I hope you got it

Answer 2

The value of theta=22.5 degrees.

Step-by-step explanation:

$sin\theta+cos\theta=\sqrt 2cos\theta$

$\theta\neq 90^{\circ}$

$\frac{sin\theta+cos\theta}{\sqrt 2}=cos\theta$

$\frac{1}{\sqrt 2}sin\theta+\frac{1}{\sqrt 2}cos\theta=cos\theta$

We know that

$sin45^{\circ}=cos45^{\circ}=\frac{1}{\sqrt 2}$

Substitute the values

$sin45sin\theta+cos45^{\circ}cos\theta=cos\theta$

We know that

$cos(x-y)=cosxcosy+sinxsiny$

Using the formula

$cos(45-\theta)=cos\theta$

$45-\theta=\theta$

$\theta+\theta=45$

$2\theta=45$

$\theta=\frac{45}{2}=22.5^{\circ}$

Hence, the value of theta=22.5 degrees.

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