Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

tan theta is equal to 2- cos theta find the value of sin theta​

Sagot :

Answer:

sqrt(2)/2

Step-by-step explanation:

Given tan(x)=2-cot(x), find sin(x).

Rewrite in terms of sine and cosine:

sin(x)/cos(x)=2-cos(x)/sin(x)

Multiply both sides by cos(x)sin(x):

sin^2(x)=2sin(x)cos(x)-cos^2(x)

Rewrite cos^2(x) using the identity sin^2(x)+cos^2(x)=1:

sin^2(x)=2sin(x)cos(x)-(1-sin^2(x))

Distribute:

sin^2(x)=2sin(x)cos(x)-1+sin^2(x)

Subtracting sin^2(x) on both sides:

0=2sin(x)cos(x)-1

Add 1 on both sides:

1=2sin(x)cos(x)

Use identity sin(2x)=2sin(x)cos(x) to rewrite right:

1=sin(2x)

Since sin(pi/2)=1, then 2x=pi/2.

Dividing both sides by 2 gives x=pi/4.

So sin(pi/4)=sqrt(2)/2

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.