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Answer 1

Given :

2θ+45° and 30°-θ are actue angles

To Find :

The degree measure of θ satisfying

$\rm\sin(2\theta+45\degree)=\cos(30\degree-\theta)$

Formula's Used :

$\sf1)\sin(90-x)=\cos\:x$

$\sf2)\cos(90-x)=\sin\:x$

$\sf3)\tan(90-x)=\cot\:x$

$\sf4)\sec(90-x)=\csc\:x$

$\sf5)\cot(90-x)=\tan\:x$

$\sf6)\csc(90-x)=\sec\:x$

Solution :

We have to Find the value of θ which satisfying the equation :

$\sf\sin(2\theta+45\degree)=\cos(30\degree-\theta)$

Let 30°- θ = x , then

$\sf\implies\sin(2\theta+45\degree)=\cos(x)$

and

We know that sin(90-x)= cos x , then

$\sf\implies\sin(2\theta+45\degree)=\sin(90\degree-x)$

$\sf\implies\sin(2\theta+45\degree)=\sin[90\degree-(30\degree-\theta)]$

Now comparing on both sides , then

$\sf\:2\theta+45\degree=90\degree-30\degree+\theta$

$\sf\implies2\theta+45\degree=60\degree+\theta$

$\sf\implies2\theta-\theta=60\degree-45\degree$

$\rm\implies\theta=15\degree$

Therefore, the value of θ is 15°

Answer 2

Value of 0(teta) will be 15°.

Go through the attachment for the answer.